{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "# Student's t distribution\n",
    "\n",
    "For more information, see chapters 9 and 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import requests\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.special import gamma, digamma\n",
    "from scipy.stats import t, norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = \"retina\"\n",
    "plt.rcParams[\"axes.spines.right\"] = False\n",
    "plt.rcParams[\"axes.spines.top\"] = False\n",
    "plt.rcParams['text.latex.preamble'] = r'\\usepackage{amsmath}'\n",
    "\n",
    "apikey = os.environ[\"AVANTAGE_API\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "Student's t distribution is defined as an ensamble of normal distributions \"weighted\" by precision terms $\\tau$ that are Gamma-distributed. That is\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "    p(x|\\mu, \\alpha, \\beta) &= \\int_0^\\infty \\mathcal{N}\\left(x |\\mu, \\tau^{-1}\\right)\\text{Gam}(\\tau|\\alpha, \\beta) \\ d\\tau \\\\\n",
    "    &= \\frac{\\beta^\\alpha}{\\Gamma(\\alpha)}\\left(\\frac{1}{2\\pi}\\right)^{1/2}\\left[b + \\frac{(x - \\mu)^2}{2}\\right]^{-a - 1/2} \\Gamma\\left(a + \\frac{1}{2}\\right)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Defining $\\nu = 2\\alpha$, $\\lambda = \\alpha/\\beta$ and rearranging, we obtain the final form of the distribution in the form\n",
    "\n",
    "$$\n",
    "    \\text{St}(x\\vert\\mu,\\lambda,\\nu) = \\frac{\\Gamma\\big((\\nu + 1)/2\\big)}{\\Gamma(\\nu/2)}\\left(\\frac{\\lambda}{\\pi\\nu}\\right)^{1/2}\\left[1 + \\frac{\\lambda(x - \\mu)^2}{\\nu}\\right]^{-(\\nu + 1)/2}\n",
    "$$\n",
    "\n",
    "* $\\nu$ is known as the degrees of freedom of the distribution;\n",
    "* $\\lambda$ is known as the precision of the distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "def students(x, mu, lmbda, nu):\n",
    "    \"\"\"\n",
    "    Generates a function that returns the value\n",
    "    of the pdf of a Student's-t distribution\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    x: float, np.array\n",
    "        Values to evaluate the pdf at\n",
    "    mu: float\n",
    "        The mean of the distribution\n",
    "    lmbda: float\n",
    "        The precision of the distribution\n",
    "    nu: float\n",
    "        The degrees of freedom of the distributino\n",
    "    \"\"\"\n",
    "    const = gamma(nu / 2 + 1 / 2) / gamma(nu / 2) * np.sqrt(lmbda / (np.pi * nu))\n",
    "    pdf = const * (1 + (lmbda * (x - mu) ** 2) / nu) ** (-nu / 2 - 1 / 2)\n",
    "    return pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
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6a61WIevAGLMI54blfKCftXZfhKfU5ET639gYE4fz6UEv4GVr7dU1XyEi9aEVehGJWdbaAoI3R37DGBNKbXsvxOKurxHlr1A0zt98VMG896Lk3/jrOMF8GTH2SZRILFBALyKx7kmc9JwkgtvPR0p5QJ9PDFWtibAzce6ZOE411WokZBH9N/avzv/C33ymAak6IlILBfQiEtP8q/Q/9DdvMcZUW/u9EZQH9Gv9tfKldjP8jw/5c/LFe5H+N/46zgZw2UT+TbdIk6QcehGReqguh96f7lN+4+DfrbXfbfTJiYhIs6QVehERb7jz51dHahIiItL8qA69iIgHrLWzcdXJFxERaSwK6EVE6ieTYJWOzMhNQ0RExKEcehERERGRGKYcehERERGRGKaAXkREREQkhimgr4Ux5nljjLZvFxEREZGopJtiazdo9OjRo4FrIj0REREREWny6l0xTSv0IiIiIiIxzLOA3hjTzRjztDFmnzGm0BiTaYz5izGmTQh9Xm+Msf6vm2s473RjzLvGmKPGmDxjzBpjzF3GmLiGji0iIiIiEgs8CeiNMX2BFcCNwFLgz8B24PvAImNMuwb02R34K3CilvMuAT4DpgGzgMeBRP8cXqrvuCIiIiIiscSrFfongI7AndbaS621d1trz8IJqgcCD9SnM2OMAf4NHAH+VsN5rYB/AqXAdGvtTdbanwAjgUXAFcaYqxvw/YiIiIiIxISQA3pjTB9gJs6OiY9XevlXwEngemNMaj26vRM4C2fF/2QN510BdABestYuL3/SWlsA/MLfvLUe44qIiIiIxBQvVujP8j9+YK0tc79grc0FPgdSgIl16cwYMxj4PfCItfazOo79fhWvfQbkAacbY1rUZWwRERERkVjjRdnKgf7HzdW8vgVnBX8AMLemjowx8cBzwC7gnlDGttaWGGN2AEOAPsCGWsZeUc1Lg+owDxERERGRiPAioE/3P2ZX83r5863r0Ne9wChgirU2v5HHFhERERGJOY2xsVR5cXxb40nGjMdZlf+jtXZRY44NYK0dU828VgCjPZqPiIiIiIinvAjoy1fB06t5vVWl807hSrXZDPyyMccWERGR5qusrIyjR4+Sm5tLYWEh1ta6BihSI2MM8fHxpKSk0KpVK9LS0sI+phc3xW7yPw6o5vX+/sfqcuwB0vzXDwYKXJtJWZxKOQD/9D/3l7qM7X+T0BsowamJLyIiIhJQVlbG7t27OXToEAUFBQrmxRPWWoqLi8nOzmb37t0cOHAg7D9bXqzQz/M/zjTG+NyVbowxLYHJQD6wuIY+CoF/VfPaaJy8+gU4Abw7Hedj4FrgPODFStdNw6mu85m1trBu34qIiIg0F0ePHiUvL4/4+HgyMjJITU3F5/Nqix5prsrKyigqKiI3N5cjR45w9OhRkpKSSE+vLqEkdCEH9NbabcaYD3Aq2dyOs7trufuBVODv1tqTAMaYBKAvUGyt3ebvIx+4uar+jTH34QT0z1prn6r08mvAQ8DVxpi/lteiN8YkAb/1n/NkqN+jiIiIND25ubkAZGRk0LJlywjPRpoKn89HUlISSUlJxMfHk5WVxbFjx6I7oPe7DVgIPGqMmYFTInICcCZOqs3PXed29b++E+gVyqDW2hxjzC04gf0nxpiXgKPAxTglLV8DXg5lDBEREWmaCgudD/BTU+uz96VI3bVq1YqsrCwKCgrCOo4nnyv5V9rHAs/gBPI/wlmFfxSYZK094sU41Yz9BnAGzkZSXwW+BxQDPwSutkqIExERkSqUhwhKs5FwKf/ZioUcegCstbuBG+twXibBcpJ16fc+4L5azvkcOL+ufYqIiIiIhJsxdQ55Q9IYdehFRKQZKS0rDRz7jK/R/qCJiDRXCuhFRCRk27O3M3v7bN7b8R67c3cHnk+OT2Z6t+lc2PdCJnWZRIIvIYKzFBFpmhTQi4hIg23P3s79C+9n5cGVVb6eX5LPe5nv8V7me7RNasv3Rn2Pr/b/qlbtRUQ8pLtARESk3qy1vLLpFb729teqDOZ9xoepdLvU0YKj3L/ofn7wyQ84XnC8kWYqIs3BCy+8wNSpU0lPTyctLY2xY8fy+OOPU1ZWVvvFlWzatIlHHnmE6667jkGDBuHzOamDr732Whhm7g2t0IuISL3kFedxz4J7mLtrbuC5eF88Z3Q7gwv7XMjUblNpEdcCgE1HNzF7x2xmb5vNwfyDAMzdNZe1h9by8PSHGdVxVES+BxFpOm6//XaeeOIJkpKSmDFjBgkJCcydO5c77riDuXPn8uqrrxIXF1fn/p588kkeeeSRMM7Ye1qhFxGROissLeT7875fIZjv17ofL13wEn858y+c3fPsQDAPMLDtQH445ofMvnw2Vw+8OvD8wfyDfPfD77L20NpGnb+INC2vv/46TzzxBBkZGaxZs4Z33nmHWbNmsWXLFgYPHsysWbN47LHH6tXn0KFD+clPfsLLL7/M1q1bOeOMM8I0e+8ooBcRkTopKSvh/336/1i8f3HguasHXs2LF7zIwLYDa7w2KT6Jn0/8OY+d9RhtWrQBIK8kj+9+9F22HNsS1nmLSNP14IMPAvDQQw/Rv3//wPOdOnXiySefBOD3v/99vVJvbr75Zv7whz9w1VVX0bdvX28nHCYK6EVEpFZltox7P7+Xj3d/HHjue6O+x88n/pyk+KQ693NG9zP493n/pnWL1gDkFOXw7Q+/za6cXV5PWUQ8YK0lKSkJYwxbtlR8833s2DFatWpFu3btOHnyZKPPbc+ePaxYsYLExESuvPLKU14/44wz6Nq1K1lZWSxevLiKHpoOBfQiIlKrp9Y+xdvb3w60bxxyI7cMu6VBffVt3Ze/nfM3UhNSATicf5g7Pr6D/JJ8T+YqIt4xxtClSxcAdu/eXeG1Nm3acO2113L06FHee++9Rp/bqlWrABgyZAjJyclVnjNu3LgK5zZVCuhFRKRGXxz6gidWPxFoXzHgCn4w5gchlZ4c0m4Ij531GElxzur+juwd/N+y/wt5riLivW7dugGnBvQAY8eOBahxBfyGG27AGFPvr8zMzBrntWPHDgB69uxZ7Tk9evSocG5TpSo3IiJSrZPFJ7n7s7sptc7ur6M6juLnE37uSR35sRljuWfCPdy78F4AXt38KpO7TmZGjxkh9y3ilV53z470FBos8/cXeNJP9+7dgaoD+tRU55O2Q4cOVXv9lClTGjRuWlpaja+fOHGiwhxq6iM3N7dBc4gVCuhFRKRav1vyO/ac2ANAWkIaD059kHifd386Lu13KfP3zufDnR8CcN/C+xjWfhgdUzp6NoaIhKamFfoNGzYA0LVr12qvv/nmm7n55ps9n5e1FkAb1aGUGxERqcZHOz/irW1vBdq/nPhLuqZV/0e7IYwx/GrSr+iU0gmA44XHuffzewN/qEUk8qoL6AsLC3n22WcBuPjiixt9Xi1btgSCK/VVKX+t/NymSiv0IiJyivySfB5a9lCgfVGfizi/z/lhGSu9RToPTn2Qm+bchMXy+b7P+Xj3x0q9kajgVdpKLKsu5eb+++9n586dnH322UycOLHa65966ikWLFhQ73Effvhh2rdvX+3rvXr1AmDnzp3VnlM+5/JzmyoF9CIicop/f/lvsk5mAdA2qS13T7g7rOONyxjH1wZ+jZc2vQTA/y37P6Z0nVJhkyoRiYyqVujfeustHnroITp06MBTTz1V4/ULFiwIrOTXx3333VdjQD9qlLPT9Lp168jPz6+y0s2yZcsqnNtUKeVGREQq2H9iP09/+XSgfeeoO2mV2Crs494x6g7SW6QDsPfEXp5b/1zYxxSR2pUH9NnZ2eTm5rJ8+XKuueYa0tLSmD17do1VZgCeeeYZrLX1/qptVb179+6MHj2aoqIiXn311VNe//TTT9mzZw8ZGRlMmjSpwd9/LFBALyIiFfxxxR8pLC0EYHDbwVza79JGGTe9RTq3j7w90P7Hmn9w4OSBRhlbRKrXqVMnEhMTAXj55Zc5++yziY+PZ86cOYE675Hys5/9DICf/vSnbN26NfD8wYMHue222wC4++678fl8p1w3aNCgwPWxTgG9iIgELM9azpzMOYH23ePvJs4X12jjXzngSvq17gc4efx/WfmXRhtbRKrm3lzqlltuITExkY8//rjGvPnGcsUVV3DrrbeSlZXFsGHDuOiii7j88svp378/69ev59JLL+WOO+445br9+/ezadMm9u/ff8prK1euZOLEiYGvlStXAnDPPfdUeD6aKIdeREQApwTco6seDbS/0usrjO40ulHnEO+L56fjf8otHzi70M7ePpubht5Evzb9GnUeIlJR9+7dyczMpH///syePZv+/ftHekoBTzzxBFOmTOHxxx/n008/pbS0lEGDBvGtb32LW2+99ZTV+drk5OSwZMmSU57fsmWLV1P2nFFpsJoZY1aMHj169IoVKyI9FRGRsFq6fyk3fXAT4ATWsy+bTZe0LhGZyx1z7+DTPZ8C8JXeX+EP0/4QkXlI01ZeQ33w4MERnok0ZQ34Oat3YX2l3IiICAB/W/O3wPGl/S6NWDAP8N0R3w0cv7/jfbZnb4/YXEREop0CehERYXnWcpZlOeXd4kwcNw29KaLzGdp+KJO7TgbAYnlqTc1l8UREmjMF9CIiwt/X/D1wfFHfi+jWslsEZ+P47vDgKv3sHbPZlbMrgrMREYleCuhFRJq51QdXs3j/YgB8xsctw26J8IwcIzuOZGJnp5JEmS3jn2v/GeEZiYhEJwX0IiLN3L++/Ffg+ILeF9CjVY8IzqYidy79O9veCexeKyIiQQroRUSasd05u/l096eB9s3Dbo7gbE41ptMYRnd0SmeW2BJe2fRKhGckIhJ9FNCLiDRjL256EYtTvnhy18n0ad0nwjM61fWnXR84fnXzqxSUFERwNiIi0UcBvYhIM5VXnMesLbMC7WsHXRvB2VRvevfpdEl1SmgeLzzOezvei/CMRESiiwJ6EZFm6q1tb3Gi+AQAvVr1CpSJjDbxvniuHnR1oP3CxhfQpogiIkEK6EVEmqEyW8bzG54PtL8+6Ov4TPT+Sbi8/+UkxSUBsPHoRlYc0O7dIiLlove3t4iIhM2ifYvIzMkEIDUhlUv6XRLZCdUivUU6F/W9KNB+YeMLEZyNiEh0UUAvItIMvbjxxcDxZf0uIzUhNYKzqZtrBl0TOJ67a65KWIqI+CmgFxFpZg7mHWT+3vmBtjs/PZr1a9OP8RnjASdl6K1tb0V4RiIi0UEBvYhIM/PWtrcos2UAjO00lp6tekZ4RnV3ef/LA8eztswKfB8iIs2ZAnoRkWbEWluhVKU7QI4FM3rMoGViSwD2nNjD8qzlEZ6RiETSpk2beOSRR7juuusYNGgQPp8PYwyvvfZapKfWqOIjPQEREWk8Kw6sYFfuLgDSEtI4u+fZEZ5R/STFJ3FB7wt4adNLAPxv6/8Y33l8hGclIpHy5JNP8sgjj0R6GhHn2Qq9MaabMeZpY8w+Y0yhMSbTGPMXY0ybevTxkDFmrjFmtzEm3xhz1BizyhjzK2NMuyrO72WMsTV8veTV9yci0hTM2hpcnT+/9/kkxydHcDYN4/5U4aOdH5FTlBPB2YhIJA0dOpSf/OQnvPzyy2zdupUzzjgj0lOKCE9W6I0xfYGFQEfgTWAjMB74PnCeMWaytfZIHbr6AbAS+BA4CKQCE4H7gG8bYyZaa3dXcd0XwBtVPP9l/b4TEZGmK7colw8yPwi0Yy3dptzgdoMZ1HYQG49upLC0kHe3vxszN/aKiLduvvnmSE8hKniVcvMETjB/p7X2r+VPGmP+hBOkPwB8tw79tLLWFlR+0hjzAHAP8DPgtiquW22tva8B8xYRaTbez3yfglLnV+yANgM4rd1pEZ5Rw13W7zIeXPog4HzqoIBeJDystSQnJ1NYWMjmzZvp379/4LVjx47Rs2dPEhIS2LVrF6mp0V/+tqkKOeXGGNMHmAlkAo9XevlXwEngemNMrf+Vqwrm/V7xP/av5nUREanFG1vfCBxf3v9yjDGRm0yILuhzAYm+RADWH1nP5mObIzwjkabJGEOXLl0A2L27YpJEmzZtuPbaazl69CjvvfdeJKYnfl7k0J/lf/zA2or1w6y1ucDnQApO6kxDlW8PuKaa17sYY75jjLnH/zg8hLFERJqc3Tm7WXPI+RUab+K5oPcFEZ5RaNJbpHNWj7MC7dnbZ0dwNiJNW7du3YBTA3qAsWPHArB48eJqr7/hhhswxtT7KzMzMyzfT1PkRcrNQP9jdcsjW3BW8AcAc+vSoTHmx0AakA6MBabgBPO/r+aSc/xf7j4+Ab5prd1VxzFXVPPSoLpcLyISzd7d8W7geErXKbROah25yXjkgj4X8H7m+wC8t+M9vj/6+/iMqjGLx+5Lj/QMGu6+bE+66d69O1B1QF+eZnPo0KFqr58yZUqDxk1LS2vQdc2RFwF9+U96dT815c+3rkefPwY6udrvAzdYayv/tOQBv8G5IXa7/7nhODfRngnMNcaMtNaerMfYIiJNirWW2TuCK9jn9zk/grPxzuQuk2mV2Iqcohz2n9zP6oOrGd1pdKSnJdLk1LRCv2HDBgC6du1a7fU333yzbl4Ns8ZYyihP0rR1vcBam2GtNUAGcDnQB1hljBld6byD1tp7rbUrrbXH/V+f4XwisAToB9TpJ8haO6aqL5yKPSIiMWvj0Y3syN4BQHJ8Mmd0axpl3RLiEpjZa2ag7f4UQkS8U11AX1hYyLPPPgvAxRdf3OjzkiAvVujLV+Cr+0yqVaXz6sxaewCYZYxZiZPS8x9gaB2uKzHGPAVMAKYB2nFARJotd6A7o8cMUhJSIjgbb13Q+wJe2+zsCDkncw4/Hf9TEnwJEZ6VNCkepa3EsupSbu6//3527tzJ2WefzcSJ1d8q+dRTT7FgwYJ6j/vwww/Tvn37el/XHHkR0G/yPw6o5vXyyjQNLkFgrd1pjFkPjDTGtLfWHq7DZeXpOaqhJCLNVmlZaYWA/vzeTSPdptzoTqPplNKJA3kHOF54nEX7FjGt27RIT0ukSalqhf6tt97ioYceokOHDjz11FM1Xr9gwYLASn593HfffQro68iLlJt5/seZxlS8G8kY0xKYDOQD1d/+XDdd/I+ldTy//K3i9hrPEhFpwlYeXMnBvIMAtGnRholdQik4Fn18xlfhTYqq3Yh4rzygz87OJjc3l+XLl3PNNdeQlpbG7Nmz6dmzZ43XP/PMM1hr6/3Vq1evRvjumoaQA3pr7TbgA6AXcHull+/HWSH/T/mNqcaYBGPMIP/usgH+5zIq92+M8fk3luoILLTWHnO9NsEYk1jFNWfhbGgF8N8Gf3MiIjHOHeCe2+vcJpmOckGfYAnOebvnkVecF8HZiDQ9nTp1IjHRCbdefvllzj77bOLj45kzZw7jxo2L8OwEvNsp9jZgIfCoMWYGsAEnf/1MnFSbn7vO7ep/fSfOm4By5wH/Z4z5DNgGHMGpdHMGzk2xWcAtlcZ9CBjiL1G5x//ccIK18X9prV0Y+rcnIhJ7isuK+WjXR4F2U6luU9mANgPom96XbdnbyC/J57M9n3Fe7/MiPS2RJqN8c6nMzExuueUWOnTowPvvv8/o0ZGvKrVy5Upuu+22QHv9+vUA3HPPPTz88MOB52uqk98UeBLQW2u3GWPGAr/GCczPB/YDjwL3W2uP1qGbj4B/4KTojMApc3kS5w3Bc8CjVfTzHHAZMA74CpAAHMDZWfYxa+380L4zEZHYtSxrGdmFzg19GakZjOwwMrITChNjDOf2PpcnVj8BwIc7P1RAL+Kx7t27k5mZSf/+/Zk9ezb9+/ev/aJGkJOTw5IlS055fsuWLRGYTeR4tUKPtXY3cGMdzsskWMrS/fyXnJqyU1tf/wL+VZ9rRESaiw93fhg4PrvH2Rhzyq/eJmNmz5mBgH7+3vnkl+STHJ8c4VmJNB2fffZZpKdQpenTp2NtnSujN1naUk9EpAkqLSvl410fB9rn9DynhrNjX9/WfemT3geA/JJ8Pt/7eYRnJCLSeBTQi4g0QSsPruRogZOl2CG5AyM7jozshBrB2T3PDhx/sPODCM5ERKRxKaAXEWmCPsgMBrQzeszAZ5r+r/uZPYO7xn66+1MKSwsjOBsRkcbT9H/Di4g0M2W2jLm75gbaTT3dptyANgPo0bIHAHkleSzatyjCMxIRaRwK6EVEmpgvDn3BoXxns+y2SW0Z3SnypeUagzGmwpsX903BIiJNmQJ6EZEmxp1uc1aPs4j3eVbQLOqd0ysY0M/bNY/i0uIIzkZEpHEooBcRaUKstRU2k2ou6TblTmt7Gl3TugKQW5zL4v1NezMZERFQQC8i0qRsPLqRrJNZALRMbMm4jOa1Lbsxhhk9ZgTan+z+JGJzERFpLAroRUSakHm75wWOp3WbRoIvIYKziYwzu58ZOP5k9yeU2bLITUZEpBEooBcRaULcAb07sG1ORnYcSesWrQE4mH+Q9UfWR3ZCIiJhpoBeRKSJ2HdiHxuPbgQg3hfP5C6TIzyjyIj3xTOt27RA271jrohIU6SAXkSkiXDni0/ImEBaYlrE5hJpFdJu9nwSuYmIiDQCBfQiIk2E0m2CTu9yOom+RAC2HNvCntw9EZ6RiEj4KKAXEWkCcopyWJ61PNA+o/sZEZxN5KUkpDCh84RA2/1mR0SkqVFALyLSBCzYs4ASWwLAae1OIyM1I8IzirwzewQ/pVBAL9I0bdq0iUceeYTrrruOQYMG4fP5MMbw2muv1en6F154galTp5Kenk5aWhpjx47l8ccfp6wstqpjNZ/tA0VEmjB3/nxzT7cpN73bdH7NrwFYeWAl2YXZpLdIj/CsRMRLTz75JI888kiDrr399tt54oknSEpKYsaMGSQkJDB37lzuuOMO5s6dy6uvvkpcXJzHMw4PrdCLiMS44rJi5u+dH2groHd0SOnA8PbDASi1pXy257MIz0hEvDZ06FB+8pOf8PLLL7N161bOOKNu6Yavv/46TzzxBBkZGaxZs4Z33nmHWbNmsWXLFgYPHsysWbN47LHHwjx77yigFxGJcasOrOJE8QkAOqd2ZkCbARGeUfRw30swf8/8Gs4UkVh0880384c//IGrrrqKvn371vm6Bx98EICHHnqI/v37B57v1KkTTz75JAC///3vYyb1RgG9iEiMc688T+s2DWNMBGcTXdz16D/f9zklZSURnI1I7LHWkpSUhDGGLVu2VHjt2LFjtGrVinbt2nHy5MkIzbD+9uzZw4oVK0hMTOTKK6885fUzzjiDrl27kpWVxeLFiyMww/pTQC8iEuM+21sxoJeggW0G0jGlI+BUAlpzaE2EZyQSW4wxdOnSBYDdu3dXeK1NmzZce+21HD16lPfeey8S02uQVatWATBkyBCSk5OrPGfcuHEVzo12CuhFRGLY7tzd7MjeAUCLuBaMyxgX4RlFF2MMU7tODbSVRy9Sf926dQNODegBxo4dC1DjSvYNN9yAMabeX5mZmWH5fnbscH5n9uzZs9pzevToUeHcaKcqNyIiMcydFz4+YzzJ8VWvNjVnU7tN5fUtrwPOpxl3jbkrshOSmDLs2WGRnkKDrf3mWk/66d69O1B1QJ+amgrAoUOHqr1+ypQpDRo3LS08u12fOOHcc1Q+95rGzs3NDcscvKaAXkQkhkVVus2uxfDpH2D/F8HnUtrCmBth7LcgISki05rUeRIJvgSKy4rZcmwL+0/sp3Na54jMRSQW1bRCv2HDBgC6du1a7fU333wzN998c3gm1wDWWoAmdb+RUm5ERGJUXnEey/YvC7Sndptaw9lhdGA9vHA1PH0ubJsLeYeDX4c3w5yfwWNjYdXzEIGKESkJKYztNDbQdpf4FJHaVRfQFxYW8uyzzwJw8cUXN/q8Gqply5ZAcKW+KuWvlZ8b7bRCLyISo5ZmLaWorAiAvul96ZpW/QpZ2Gx8F175BpQV13xe9m548zbY8gF89V8Q17h/fqZ1m8ai/YsAJ03pqoFXNer4Eru8SluJZdWl3Nx///3s3LmTs88+m4kTJ1Z7/VNPPcWCBQvqPe7DDz9M+/bt631dbXr16gXAzp07qz2n/HstPzfaKaAXEYlRlctVNrptH8Or33QF8waGXwVTfggp7cCWwfo3nDScvMPOKevfgPgkuPRJ8DXeh8TTuk3joWUPAbAkawmFpYW0iGvRaOOLxLKqVujfeustHnroITp06MBTTz1V4/ULFiwIrOTXx3333ReWgH7UqFEArFu3jvz8/Cor3SxbtqzCudFOKTciIjHIWlshdaTR0212LoQXr4FS5xMC2vaB7y6Ay/8BHQdBWgdo2QkmfAe+v9rJoS+35iV490fgz2NtDD1a9aBXq14A5JfksyxrWc0XiEhAeUCfnZ1Nbm4uy5cv55prriEtLY3Zs2fXWC0G4JlnnsFaW++vcK2Od+/endGjR1NUVMSrr756yuuffvope/bsISMjg0mTJoVlDl5TQC8iEoO2Ht9K1sksAFomtGRkx5GNN/jBjfD8VVCS77TTu8M33oKMoVWf36IlXPAnGHND8LnlT8O834V9qm5TugYrbXy+9/NGHVsklnXq1InExEQAXn75Zc4++2zi4+OZM2dOoF57rPnZz34GwE9/+lO2bt0aeP7gwYPcdtttANx99934GvGTxFDExixFRKSChfsWBo4ndplIgi+hcQYuLYE3boUifym3tE7wjTehdfearzMGLvgzDP9a8Ln5D8PeFeGbayUVAvp9CuhF6sq9udQtt9xCYmIiH3/8cY15841l5cqVTJw4MfC1cuVKAO65554Kz1d2xRVXcOutt5KVlcWwYcO46KKLuPzyy+nfvz/r16/n0ksv5Y477mjsb6fBlEMvIhKDFuwN3mDmDlTDbvETsM/5g0lcIlz3OrTrW7drfT645AnI3Q87PnNy7N+8A779KcQnhm/OfmM6jSHRl0hRWRE7sneofKVIPXTv3p3MzEz69+/P7Nmz6d+/f6SnBEBOTg5Lliw55fktW7bUeu0TTzzBlClTePzxx/n0008pLS1l0KBBfOtb3+LWW2+NmdV5UEAvIhJz8orzWHEguLJ9epfTG2fgI9tg3gPB9hn/DzLquelOXDxc/Fd4YhIU58HB9TD/j3Dmz7ydaxWS4pMY02lMoNrNwn0L+eqAr4Z9XJGm4LPPonOX5enTpwfqyjfENddcwzXXXOPhjCIjdt56iIgIAMsPLKfYX1mmX+t+ZKRmhH/QsjJ463tQUuC0M4bB5Lsa1lebXjDj3mB7/sOQ9WWoM6yTyV0nB46VdiMiTYUCehGRGONOt5ncZXINZ3roixdhpz8ANnFwyeMQF0Le/vhvQ7fxznFZCbxzV6NUvXF/mrF4/2JKykrCPqaISLgpoBcRiTHuCi3uFeewKSmCT38fbE/+PnQeEVqfvvI3Bf7c+T3LYMuHofVZB/1a96NjckcAcoty+fJw43wyICISTgroRURiyK6cXezK3QVAcnwyozuNDv+gq5+H486YpLSDqT/ypt8OAyrWp5/3QNhX6Y0xTOoSrCu9aN+isI4nItIYFNCLiMQQd973uIxx4d/ttKQQPns42J78fWiR5l3/U37g7BwLsH81bHrPu76roTx6EWlqPAvojTHdjDFPG2P2GWMKjTGZxpi/GGPa1KOPh4wxc40xu40x+caYo8aYVcaYXxlj2tVw3enGmHf95+cZY9YYY+4yxsR5892JiESHCuk2jZE/v/I/kLPHOU7tAONu9rb/lhkw9qZg+5PfhX2VflLnSRgMAGsPryW7MDus44mIhJsnAb0xpi+wArgRWAr8GdgOfB9YVFMwXskPgFTgQ+AR4HmgBLgPWGOMOWXnEmPMJcBnwDRgFvA4kOifw0sN/qZERKJMUWkRS7OWBtphrz9fXADz/xRsT74LElO9H2fKXRCf7BxnrYWN73g/hkvrpNYMaTcEgDJbxpL9p9awFhHxQiglNevDqxX6J4COwJ3W2kuttXdba8/CCaoHAg/UeHVQK2vtRGvtt/x9fM9aOw74HdAFqFCo2BjTCvgnUApMt9beZK39CTASWARcYYy52otvUEQk0r449AX5JfkAdEvrRo9WPcI74KrnIHefc5zWqWK+u5fSOsL4W4LtT34f9lX607sGq924d92V5sUY55OasrKyCM9Emqryn63yn7VwCTmgN8b0AWYCmTir426/Ak4C1xtjal3WsdYWVPPSK/7HytuSXQF0AF6y1i6v1M8v/M1baxtXRCQWuG/gdN/YGRZlZbDkb8H25LsgMSV8403+PiT4+z/wJWQuqPn8ELnLVy7ct7DRVtEkurRo4dyDcvLkyQjPRJqqnJwcAJKSksI6jhcr9Gf5Hz+w1lZ4i2utzQU+B1KAiSGMcZH/cU01Y79fxTWfAXnA6caYMN81JiISfo0a0G+fB0e2OsctWsHob4R3vNT2MML1gerSf4R1uOEdhpOa4Kwz7T+5nx05O8I6nkSnli1bApCVlUVubi5lZWV6cychsdZSVlZGQUEBhw4dIisrC4A2bep8S2mDxHvQx0D/4+ZqXt+Cs4I/AJhblw6NMT8G0oB0YCwwBSeY/32lU6sd21pbYozZAQwB+gAbahlzRTUvDarLnEVEwim7MJt1R9YB4DM+xmeMD++A7oB65LXeVrapzvhvw/KnneONsyF7D6R3C8tQCb4EJmRM4OPdHwOwcO9C+qT3CctYEr3atm3LyZMnycvLY8+ePZGejjRRbdu2pVWrVmEdw4sV+nT/Y3VlAsqfb12PPn+Mk65zF04w/z4w01p7qBHGFhGJOkv2L8HirBwOaTeE9BbptVwRgqM7YPOcYNvryjbV6TgYek11jm0pLP93WIdT+Urx+Xx0796dDh06kJSUFPY8Z2kejDEkJCSQnp5O9+7d6dSpU9h/trxYoa9N+XdQ58+wrLUZAMaYTsDpOCvzq4wxF1prV4ZjbGvtmCo7cFbuG2HnFhGR6i3evzhwPLFzKBmMdbD8XwR+bfY7G9r3C+94buO/DZnzneMVz8C0n0BCeHJP3WlLy7OWU1RaRGL5zrXSbPh8Ptq3b0/79u0jPRWRBvNihb58Fby65aJWlc6rM2vtAWvtLJyUnXbAfxprbBGRaNJo+fNFebDyuWB7/LfDN1ZVBp4PrfxpNnmHYf0bYRuqe8vu9GjpVAoqKC1g5cH6rBeJiEQPLwL6Tf7HAdW8Xl6Zproc+1pZa3cC64Ehxhj3W+hqxzbGxAO9cerYb2/o2CIikbY7dzd7Tjj5vcnxyYzoMCJ8g619FQqOO8dtekG/c8I3VlXi4mGcqzzmkr+HdbgK1W72qnyliMQmLwL6ef7HmcaYCv0ZY1oCk4F8YHHlC+upi/+x1PXcx/7H86o4fxpOdZ2F1trCEMcWEYkY9+r8mE5jwpsWstL1Qei4m8Hn2YbidTf6mxDnL062byUcWBe2oZRHLyJNQci/qa2124APgF7A7ZVevh9n59f/WGtPAhhjEowxg/y7ywb4n8uo3L8xxmeMeQBn46qF1tpjrpdfAw4DVxtjxrquSQJ+628+Gcr3JyISae78+Umdw5huc3gL7PVv6eFLgBHXhG+smqS2h0HnB9urXwjbUOMyxhFvnNvJNh/bzKG8yrUXRESin1dLL7cBB4FHjTFvGGMeNMZ8DPwAJ9Xm565zu+KUkKxcwvI8YLcxZq4x5h/+Pp7GKXt5D5AF3OK+wFqb438uDvjEGPOUMeYPwGpgEk7A/7JH36OISKMrLStlyf4lgXZY8+fdgfOAcyG1XfjGqo37zcSaV6C0JCzDpCakMrLjyEBbu8aKSCzyJKD3r9KPBZ4BJgA/AvoCjwKTrLVH6tDNR8A/cG5+vRz4CfBV4CjOSv8Qa+36KsZ+AzgDZyOprwLfA4qBHwJXW+0QISIxbMPRDeQUOTsNtk9uT7/WYao4U1YKa1zrHyMjtDpfru9ZkNbJOT55ELZ9XPP5IXCn3bg/DRERiRWela201u4GbqzDeZkEy0m6n/+SU1N26jr258D5tZ4oIhJj3PnzEztPDF8t4x2fQc5e5zilXePfDFtZXDwMvwoW/tVpf/ECDJgZlqEmdZ7EIzwCOAG9tVb1yEUkpkTgbicREamrRfsbqVzlFy8Gj4ddCfFRUI/dnXaz8V3IP1b9uSEY1HYQLRNbAnA4/zDbs1UYTURiiwJ6EZEolVecx6qDqwLtsG0oVZgLG94Otkd8PTzj1Fen06Czv0RnaSGsmxWWYeJ8cYzPGB9oK+1GRGKNAnoRkSi18uBKSsqcm0H7te5Hx5SO4Rlo/ZtQnOccd3QF0dHAvUq/+sXqzwuR+82SAnoRiTUK6EVEolTl/PmwWfNK8HjE1yGa8seHXQE+/+1ee5bC0R1hGWZC5wmB4+VZywNvpEREYoECehGRKNUo+fMnDkLmfH/DOAF0NEltD/3ODrbDlHbTq1UvOqU4VXVOFJ9g3ZHwbWYlIuI1BfQiIlHocP5hthzbAkC8L56xncbWckUDbXgLbJlz3GMStOpS8/mRMOSy4HGYAnpjTIVVenftfxGRaKeAXkQkCrnTbUZ0GEFKQkp4Blr3RvB46OXhGSNUA8+HuBbOcdYaOLItLMMoj15EYpUCehGRKOQOKCd1DlO6TW4WZC7wNwwMvjg844QqqVWltJv/hWUY9wr96oOryS/JD8s4IiJeU0AvIhJlrLUs3ucK6MOVP7/+LcC/mXavKdCyU3jG8UKFtJs3wjJEx5SO9E3vC0BxWTGrDqyq5QoRkeiggF5EJMpsz97OwfyDALRMaMmQdkPCM5B7pdsdMEejgedBfJJzfOBLOLQ5LMO4V+kXZyntRkRigwJ6EZEo474hc1zGOOJ8cd4PkrMPdvnz9I0vetNtyrVoCf3PCbbDdHNshTz6fQroRSQ2KKAXEYky7oDevWLsKXfaSu9pkNYhPON4aYjrpt0w5dGPzRiLzzh/Gjce3Uh2YXZYxhER8ZICehGRKFJaVsqyA8sC7bBtKLX+zeBxtKfblBtwLpRX+zm0EQ5u9HyIloktGdp+KAAWy9KspZ6PISLiNQX0IiJRZOOxjeQW5QLQIbkDvdN7ez9I7gHY7f8UwPhg0IXejxEOiakVq91sfDssw0zIcOXRK+1GRGKAAnoRkSjiTrcZ33k8xhjvB9n0LoHqNj1Od3ZjjRWDLwoeb5wdliHcVYWWZGmDKRGJfgroRUSiyNL9wRQP90qxpza+EzweHCOr8+X6zwRfvHO8bxVk7/F8iBEdRpAU51TU2Zmzk/0n9ns+hoiIlxTQi4hEieLSYlYeXBloj+883vtBCrJh+6fB9qALvB8jnJJbOzfxlgvDKn1iXCKjOo4KtLVrrIhEOwX0IiJRYs3hNYHdSbuldaNrWlfvB9nyIZQVO8edR0DrHt6PEW7unP8N4cmjn9jFVb5SAb2IRDkF9CIiUaJCuk24ylW6A+BYuRm2soHnB493LoS8o54P4f73X7J/CdZaz8cQEfGKAnoRkSjhXgkenxGGdJviAtj6UbAdqwF9q87QbZxzbEth03ueDzGozSDSW6QDcKTgCFuPb/V8DBERryigFxGJAnnFeaw5vCbQDkv+/I5PoeiEc9y2D3Qc7P0YjcX9ZsR9k69H4nxxFd5UuasPiYhEGwX0IiJRYPXB1ZSUlQDQr3U/2ieHoZRk5XSbcJTEbCzu8pXbPobCE54P4d7US3n0IhLNFNCLiESBxVlhTrcpK4PN7wfbsZpuU65dX+jg/4ShpAC2f+L5EO48+hUHVgTecImIRBsF9CIiUSDsN8TuXQEnDznHqR2g21jvx2hsA78SPHa/WfFIj5Y96JTSCYATxSdYf2S952OIiHhBAb2ISIRlF2az4egGAHzGx9iMMATbm103jvY/F3xx3o/R2AacFzze8oHzKYSHjDEV3lwtzVpaw9kiIpGjgF5EJMKWH1hOmXWC0dPankarxFbeD7LJtYI98Lzqz4sl3cZCclvn+MQB2L/a8yHcAb3y6EUkWimgFxGJMHe6TViq2xzbCQfXOcdxLaDPmd6PEQm+OOg/M9jePMfzIdz3M6w+uJrC0kLPxxARCZUCehGRCHOXRJyQEYb8eXd+ee9p0CLN+zEiZcC5weMw5NFnpGbQq1UvAApLC/ni4BeejyEiEioF9CIiEXQ4/zDbsrcBEO+LZ1SnUd4P4t54qamk25TrNwN88c7x/tWQs9/zISrUo89SPXoRiT4K6EVEIsidbjOiwwiS45O9HaAgBzIXBNsDmlhAn5QOPU8Ptrd4n3bjzqPXBlMiEo0U0IuIRJB7xTcs6TbbPoayYuc4Yzikd/N+jEhzv0kJQx79uIxxgeMvD3/JyeKTno8hIhIKBfQiIhFUIX8+HPXn3Xnl7rrtTYk7oN/+CRTne9p9m6Q2DGo7CIBSW8qKAys87V9EJFQK6EVEImRP7h72ntgLQHJ8MsPaD/N2gLJSpz57uaaWblOuXV9o1885Ls6rmGLkkQp59Eq7EZEoo4BeRCRC3BsVje40moS4BG8H2LsS8o44x2mdoPNIb/uPJhXSbryvdqMNpkQkmimgFxGJkLCXq3Svzvc7B3xN+Fd+5Tx6az3tfkynMcQZZ3fdjUc3cqzgmKf9i4iEogn/dhcRiV7W2gorvWHZUMpd8WXAzOrPawp6TIQW6c5x9m44sM7T7lMTUhnafmigvSxrmaf9i4iEwrOA3hjTzRjztDFmnzGm0BiTaYz5izGmTR2vb2eMudkYM8sYs9UYk2+MyTbGLDDG3GSMOWWuxphexhhbw9dLXn1/IiJe2p69ncP5hwFoldiKQW0GeTtAbhbs92+C5ItvOrvDVicuwalJXy7MaTfKoxeRaBLvRSfGmL7AQqAj8CawERgPfB84zxgz2Vp7pJZurgSeBPYD84BdQCfgcuAp4CvGmCutrfJz1C+AN6p4/sv6fzciIuHnDgjHZYwjzhfn7QBbPgwe95gESa287T8aDTgP1v3POd48B6b92NPuJ2RM4B9r/gEoj15EoosnAT3wBE4wf6e19q/lTxpj/gT8AHgA+G4tfWwGLgZmW2vLXH3cAywFvooT3L9exbWrrbX3hfINiIg0JndA766g4pkK6Tbnet9/NOp3Nhgf2DLYswxOHobU9p51P6LjCFrEtaCwtJDMnEyyTmaRkZrhWf8iIg0VcsqNMaYPMBPIBB6v9PKvgJPA9caY1Jr6sdZ+bK192x3M+5/PAv7mb04Pdb4iIpFWWlbKsgPBHOyJnSd6O0BJEWz7JNju38Tz58ultoNu5W+ObMVPKTzQIq4FIzuODLS1Si8i0cKLHPqz/I8fVBGM5wKfAylAKH+x/NscUlLN612MMd8xxtzjfxwewlgiImG18dhGcotyAWif3J7e6b29HWDXIvD3T+ue0H6At/1Hs4HhLV/pfvOlPHoRiRZepNwM9D9urub1LTgr+AOAufXt3BgTD3zD36zut/M5/i/3dZ8A37TW7qrjONVt/efxnWoi0txVTrcxxng7gLtcZf+Z4HX/0WzAefDRfc7x1rnOpxXxiZ51X3mDKWut9//9RETqyYsVen+dMLKreb38+dYN7P/3wFDgXWvtnEqv5QG/AcYAbfxfZ+DcVDsdmFtbqo+ISGNbuj+YquF5ug1U2h22meTPl+swCFr3cI6LcmHXQk+7P63daaQlpAFwIO8Au3LrtGYkIhJWjVGHvnzpot67fBhj7gR+hFM15/rKr1trD1pr77XWrrTWHvd/fYbzicASoB9wc13GstaOqerLP7aIiCeKS4tZeXBloO15/fmjO+Cw/wPT+GToNcXb/qOdMRU3mfI4jz7eF8/YTmMDbaXdiEg08CKgL1+BT6/m9VaVzqsTY8ztwCPAeuBMa+3Rul5rrS3BKXUJMK0+44qIhNOaw2vIL8kHoFtaN7qmdfV2AHcA23saJCR7238scN8EvLnyB7uhc78JU0AvItHAi4B+k/+xuruu+vsfq8uxP4Ux5i7gMZw68mf6K93U1yH/o1JuRCRqVMifD/fusP3Pqf68pqzXFOfTCYAjW+Dodk+7d28wtTRrKWUV60GIiDQ6LwL6ef7HmZV3czXGtAQmA/nA4rp0Zoz5KfBnYDVOMH+wgfMqT0z19je5iEgI3AH9hIwJNZzZAEV5sGN+sN1cylVWlpDsfDpRzuO0m36t+9E2qS0AxwuPs+XYFk/7FxGpr5ADemvtNuADoBdwe6WX78dZIf+PtfYkgDEmwRgzyL+7bAXGmF/i3AS7AphhrT1c09jGmAnGmFPKFxhjzsLZ0Argv/X7jkREwiOvOI81h9cE2p6v0O/4DEoLneMOg6BNT2/7jyUDXG9m3DcJe8BnfBWq3SzeX6f1KhGRsPFqp9jbgIXAo8aYGcAGYAJwJk6qzc9d53b1v74T500AAMaYbwK/BkqB+cCdVZQCy7TWPuNqPwQM8Zeo3ON/bjjB2vi/tNZ6W+JARKSBVh5cSUmZs51Gv9b9aJ/s3S6mwKnlKpsz9/e/Yz4UnYRE7zIwx3cez/uZTiXlpVlL+eaQb3rWt4hIfXkS0FtrtxljxuIE5OcB5wP7gUeB++t4Q2v5zipxwF3VnPMp8Iyr/RxwGTAO+AqQABwAXgEes9bOr9yBiEikuMtVuvOwPWGtAnq31j2gw2A4tMH51GLH/IqbToXInS61PGs5xWXFJPgSPOtfRKQ+vFqhx1q7G7ixDudlEixl6X7+PuC+eo75L+Bf9blGRCRS3KkZnufPH9oI2bud4xbp0CMM9e1jTf9znIAenJuFPQzou7fsTufUzuw/uZ+8kjzWHV7HyI4jPetfRKQ+GqMOvYhIs5ddmM3Go862Fj7jY2zG2FquqCd3eca+Z0KcVosrbKq15UPnUwyPGGMq5NEvzVpaw9kiIuGlgF5EpBEsy1qG9e+vN6TdEFomtvR2AHcll+aeblOu+wTn0wpwPr04uMHT7t1pU6pHLyKRpIBeRKQRVEi38Tp/Pv847FoUbDfX+vOVxSU4n1aU87jajfu/4+qDqykoKfC0fxGRulJALyLSCCrUn/c6oN8+D2ypc9xlFKR19Lb/WNY/fOUrO6Z0pHe6U8+hqKyI1YdWe9q/iEhdKaAXEQmzAycPkJmTCUCiL5GRHUZ6O8Bmd3Wbc6s/rzlyf1qxa7HzaYaHKuTR71cevYhEhgJ6EZEwc98wObLjSJLik7zrvKwMtip/vlppHZ1PLcD5FGPbx552rzx6EYkGCuhFRMIsrOk2+1fByUPOcUr7YPAqQf0rVbvx0LhO4zD+SsxfHvmS3KJcT/sXEakLBfQiImFkrWVJVhgD+grpNueAT7/WT+H+1GLrh86nGh5pndSaQW0HAVBmy1hxYIVnfYuI1JV+84uIhNGu3F1kncwCIDUhlSHthng7gHaHrV2XUc6nF+B8mrF/lafdK+1GRCJNAb2ISBi5A7yxncYS7/Nsg244cRD2rXSOTRz0Pcu7vpsSn6/izbGbva12ow2mRCTSFNCLiIRRWPPnt34UPO4xEZJbe9t/UxLG8pVjOo0h3jhv1DYf28yR/COe9i8iUhsF9CIiYVJmyyqs2LpXcj2xeU7wWJtJ1azvWc6nGOB8qnHioGddpySkMKzDsEB72YFlnvUtIlIXCuhFRMJky7EtHC88DkDbpLb0b9Pfu85Li2HbvGBb9edrltza+RSjnPvTDQ+436wpj15EGpsCehGRMFm8f3HgeHzGeHzGw1+5uxZDYbZznN4dOg72ru+myv0phsdpN+50Km0wJSKNTQG9iEiYuFdqx3f2Ot3m/eBx/5lgjLf9N0XuTzG2fux8yuGRER1GkBTnbBi2K3cX+0/s96xvEZHaKKAXEQmD4rLiCjXJJ2ZMrOHsBnCvMA84z9u+m6qOg6FVN+e4MBt2e7eSnhiXyKiOwU293HsPiIiEmwJ6EZEwWHd4HXkleQB0Se1Ct5bdvOv8yDY4vNk5jk+G3lO967spMwYGuKvdzKn+3AZwfwqjPHoRaUwK6EVEwqBC/nzn8RgvU2Lcq/N9zoCEZO/6buoqlK/80NOuJ3YOfgqzdP9SrLWe9i8iUh0F9CIiYeAuV+l5/Xl3ucoBqm5TL72nQVwL5/jgeji+27OuB7UdRMuElk7X+QfJzMn0rG8RkZoooBcR8Vh+ST6rD64OtCdkeBjQF+ZC5oJgW+Uq6ycxFXpNCbY9rHYT74tnTMaYQFtpNyLSWBTQi4h4bNXBVRSXORVU+qT3oUNKB+863zYP/H2TMQzSu3rXd3Ph/lTD4/KVFdJuslS+UkQahwJ6ERGPueuQhzXdRqvzDeOuR7/9Uygu8Kxr9wZTS7OWUmbLPOtbRKQ6CuhFRDzmTrXwNKAvK1O5Si+07QPt/Lv2luRXTGEKUb/W/Wib1BaA7MJsNh3d5FnfIiLVUUAvIuKhnKIc1h9dD4DP+Bjbaax3ne9fBScPOscp7aHraO/6bm7c1W7cm3SFyBhT4Z4J5dGLSGNQQC8i4qHlWcsDaRaD2w4mvUW6d51XSLc5B3xx3vXd3Ljz6De/Dx6WmHR/KqMNpkSkMSigFxHxUNjSbUDlKr3U83Qof7OVvRsOfOlZ1+4NplYcWEFxabFnfYuIVEUBvYiIh8IW0Ofsh/2rnWNfPPQ9y7u+m6O4BOh/drC9ybu0m25p3eiS2gVwSph+ecS7NwsiIlVRQC8i4pHD+YfZlr0NgARfAqM6jvKuc/fNsD1PhyQPU3maq4HnB483vetZt8aYimk3yqMXkTBTQC8i4hF34DaiwwiS45O969wd0KtcpTf6zQDjvw9h30rIzfKsa3fajQJ6EQk3BfQiIh5ZvH9x4Ngd0IWsuMDZUKqcylV6I7mN82lHOQ+r3bgr3aw+tJq84jzP+hYRqUwBvYiIB6y1LNq3KNCe1HmSd53vXADFJ53jtn2hfT/v+m7uBn4leOxhHn2HlA70a+38dyopK2HFgRWe9S0iUpkCehERD+zI2cGBvAMAtExoydD2Q73rXNVtwscd0G+fB0XeraRP7DwxcLxo/6IazhQRCY0CehERD7hX58dljCPeF+9Nx9YqoA+ntn2g/UDnuKQAdnzqWdeTugQ/pXH/fIiIeE0BvYiIBxbvC+bPuwO5kB3aCMd3OseJLaHH6TWfL/VXIe3Gu2o3YzuNDbyx23p8K4fyDnnWt4iImwJ6EZEQFZcVszRraaB9ehcPg+6N7wSP+50F8Yne9S0Od0C/eQ6UlXnSbUpCSoXSpUq7EZFw8SygN8Z0M8Y8bYzZZ4wpNMZkGmP+YoxpU8fr2xljbjbGzDLGbDXG5Btjso0xC4wxNxljqp2rMeZ0Y8y7xpijxpg8Y8waY8xdxhjtiy4iYbfm0BrySpzc665pXenesrt3nW90rRgPusi7fiWo2zhIaeccnzgA+1Z51rX75mil3YhIuHgS0Btj+gIrgBuBpcCfge3A94FFxph2dejmSuCfwARgCfAX4HVgKPAU8IoxxlQx9iXAZ8A0YBbwOJDon8NLoXxfIiJ14Q7UJnaeSBW/qhome69THx2c3WH7n+NNv1KRL65ibf/N73nWtTv9avH+xVhrPetbRKScVyv0TwAdgTuttZdaa++21p6FE1QPBB6oQx+bgYuBbtbaa621P7PWfgsYBOwGvgpc7r7AGNMK501AKTDdWnuTtfYnwEhgEXCFMeZqT75DEZFquFMpPM2fd+dz95oCya2961sqqpBH711AP7jtYNJbOLv6Hs4/zJbjWzzrW0SkXMgBvTGmDzATyMRZHXf7FXASuN4Yk1pTP9baj621b1tryyo9nwX8zd+cXumyK4AOwEvW2uWuawqAX/ibt9b5mxERqaecohy+PPwlAAZTYUOhkG2cHTwedKF3/cqp+p4Fcf77Ew58Ccd3edJtnC+uws+E0m5EJBy8WKE/y//4QRXBeC7wOZACTKx8YT0U+x9Lqhm7qt1APgPygNONMS1CGFtEpFpL9y+lzP+rb0i7IbROau1Nx/nHIXN+sO1eQRbvtUiD3tOCbQ83mVL5ShEJNy8Cen8BXzZX83r554sDGtK5MSYe+Ia/Wfk3bLVjW2tLgB1APNCnIWOLiNSmwu6wXqbbbP0IyvxrGF1GQXo37/qWqg04L3gcpjz6FQdWUFha6FnfIiLgTUCf7n/Mrub18udbN7D/3+PcGPuutXZOpdc8G9sYs6KqL5wcfhGRKoUtf95drnLQBd71K9VzB/Q75kNBjifddk3rSs9WPQEoKC1g9cHVnvQrIlKuMerQl5d7qPet/caYO4EfARuB6xtzbBGR2uzO3c3u3N0AJMcnM6LDCG86LimELR8G2wMV0DeK1t0hY5hzXFYM2z72rOuJnYNZp0q7ERGveRHQl6+Cp1fzeqtK59WJMeZ24BFgPXCmtfZoOMe21o6p6gvnzYSIyCncgdmYTmNIjPNo06cdn0HRCee4TW/oONibfqV2A1z3KrhvSg6R+9ObhfsWetaviAh4E9Bv8j9WlyPf3/9YXY79KYwxdwGPAV/iBPNZ9R3bn3vfG+dG2u11HVtEpK4W718cOPZ2d1h3dZsLwKu69lI7d3rT5jlQUuRJt+MzxhPn3+tw49GNHCs45km/IiLgTUA/z/84s/JursaYlsBkIB9YXPnCqhhjfopTv341TjB/sIbTyz8PPa+K16bhVNdZaK3VHUgi4qnSslKW7F8SaLt3BA1JWVnF+vMqV9m4Oo+A1j2c48Js59MSD7RMbMmw9k46j8VW+NkREQlVyAG9tXYb8AHQC7i90sv3A6nAf6y1JwGMMQnGmEH+3WUrMMb8Eucm2BXADGvt4VqGfw04DFxtjBnr6icJ+K2/+WS9vykRkVqsP7KenCLnpsmOyR3p2/qUX2kNs3cFnDjgHKe0h+7jvelX6sYYGHxxsL3hTc+6rlC+cr/y6EXEO/Ee9XMbsBB41BgzA9gATADOxEm1+bnr3K7+13fivAkAwBjzTeDXOLu+zgfurGL79Exr7TPlDWttjjHmFpzA/hNjzEvAUZwdZwf6n3/Zo+9RRCTAHZBN7DKRKn5fNYy7us3A88AX502/UneDL4ZFjznHG2fDBX+GuND/XE7qMoknv3DWmBbtW4S11rufGxFp1jwJ6K212/wr5L/GSX85H9gPPArcX80NrZX19j/GAXdVc86nwDOVxn7DGHMGzpuGrwJJwFbgh8Cj1lpVuBERz7lvbHRXMAmZdoeNvG7jIC0DTmRB3hHYtQh6Tw2526Hth5KakMrJ4pPsP7mfzJxMeqf3rv1CEZFaeFa20lq721p7o7W2s7U20Vrb01r7/crBvLU201prrLW9Kj1/n//5mr6mVzP259ba8621bay1ydbaYdbaP1trS736/kREyuUV5/HFoS8Cbc/qzx/aDEf8e/ElpECf6d70K/Xj88Fg15upDW950m2CL4HxGcEUKpWvFBGvNEYdehGRJmX5geWU+HdxHdBmAO2T23vT8SbX6ny/GZCQ7E2/Un8V8ujfdm5W9oDy6EUkHBTQi4jUk3tl1bPqNqB0m2jSczIkt3WOc/c7Nyt7wP3zsixrGcVlxZ70KyLNmwJ6EZF6WrB3QeDYs3Sb3CzYs8w5NnHQf6Y3/UrDxMXDoPODbY+q3fRs1ZMuqV0AOFl8ki8OflHLFSIitVNALyJSD3ty95CZkwlAUlwSYzPG1nxBXbmr2/Q8HVLaetOvNNzgS4LH698CD2osGGOY3HVyoO1+cygi0lAK6EVE6sEdgI3LGEeLuBbedLzujeDxaZdUe5o0oj5nQItWzvHxnZC11pNup3SdEjhWQC8iXlBALyJSD+4AzL3SGpITh2Dn5/6GgcEXedOvhCa+BQw4N9j2qNrNhM4TiPc5VaM3HdvEwbyaNkQXEamdAnoRkToqKi1iadbSQHtq19BrkwNOuo31V1HpMQlaZnjTr4TOXe1mvTcBfWpCKqM7jg60P9/7eQ1ni4jUTgG9iEgdrTiwgvySfAB6tOxBj1Y9vOl4/RvBY6XbRJd+MyDeXz708CY4tMmTbpV2IyJeUkAvIlJH7sDLHZCF5OQR2DE/2Fa6TXRJTIX+ZwfbHqXduH9+Fu1fFNjXQESkIRTQi4jUUVgC+o3vQPmm1t0nQHpXb/oV71SuduOBfq370TGlIwC5RbmsPezNDbci0jwpoBcRqYN9J/axPXs7AIm+RO/KVa531TdXuk10GjATfAnOcdYaOLoj5C6NMRXuwZi/Z34NZ4uI1EwBvYhIHVQuV5lcnlcdiryjsOPTYNt9A6ZEj6R06HtmsO3eMyAEyqMXEa8ooBcRqYPwpNvMhvLc6a5joXV3b/oV77nfbLn3DAjBhM4TiDdO+coNRzdwOP+wJ/2KSPOjgF5EpBbFpcUs2b8k0PYsoP/y9eDxkEu96VPCY9AF4K8dz97lcCwz5C5bJrZkRMcRgfbCfQtD7lNEmicF9CIitVh5cCV5JXkAdEvrRs9WPUPv9MShiuk2Qy4LvU8Jn5S20PesYHvdLE+6rZB2s0dpNyLSMAroRURq4d74Z3LXyRhjQu90w5sVN5NK7xZ6nxJeQ78aPHZ/uhIC942xC/cvpLSs1JN+RaR5UUAvIlKL+XuDFUg82x32y/8Fj92BokSvgedDXAvnOGstHNoccpcD2gygQ3IHALILs1W+UkQaRAG9iEgNsk5msfX4VgASfAmMyxgXeqfZe2GnP1/a+FSuMlYktYL+5wTb6/5X/bl1ZIxhctfJgfbn+z6v4WwRkaopoBcRqYG7us3YTmNJSUgJvdP1bwDWOe49DdI6ht6nNI7KaTfWhtyl8uhFJFQK6EVEauAO6N0rqSFx518r3Sa2DDgXElKd48Ob4cCXIXc5qcsk4kwcAOuOrONowdGQ+xSR5kUBvYhINYrLilm8f3Gg7Un+/NEdsHeFc+xLgEEXht6nNJ7EVBj4lWDbg5tjWyW2YniH4QBYbIWbsEVE6kIBvYhINVYfXM3J4pMAdEntQu/03qF3+uVrweN+M5xyiBJb3J+qrH0dyspC7tKddqM8ehGpLwX0IiLVqLw7bMjlKq2FNa8E20OvCK0/iYx+MyCptXOcvQt2L67x9LpwB/QL9y6kzIb+JkFEmg8F9CIi1XCXq/Rkd9j9q528a4DENGf3UYk98S0qbgS25uWQuxzUdhDtktoBcKzwGF8eDj03X0SaDwX0IiJV2HtiL1uObQEg0ZfIhM4TQu/UvTo/+CJI9KBijkTG8K8Fj9fNgpLCkLrzGR9TuwXv0fhk9ych9ScizYsCehGRKrgDqvGdx4derrK0BNa68ueHXxVafxJZ3SdA6x7OcUE2bPkg5C6nd5seOP5kzych9ycizYcCehGRKrgD+jO7nxl6hzs+gZMHneO0DOh9Ruh9SuT4fDDM9abMg7SbSV0mkehLBGDLsS3syd0Tcp8i0jwooBcRqSS3KJflB5YH2tO6TQu9U3e6zbArwBcXep8SWe60m81zIP9YSN2lJKRUSO36dM+nIfUnIs2HAnoRkUo+3/c5JWUlAAxuO5iM1IzQOiw8ARveDrbdgaDErg4DoMso57i0CNa/GXKX07tPDxwrj15E6koBvYhIJZ6n22ycDcV5znGHwZAxLPQ+JTq435x98VLI3Z3RLZiKtTxrOblFuSH3KSJNnwJ6ERGXkrIS5u8Jlqt0r5g22Orng8fDr4JQ69lL9Bj6VTD+9Kldi+DItpC665TaidPanQZAiS3RrrEiUicK6EVEXFYdXEVOUQ4AnVI6MajtoNA6PL4LdnzmHBsfjLg6xBlKVEnrCP3PCba/eDHkLt1vIuftnhdyfyLS9CmgFxFxcafbTO8+PfTdYVe/CFjnuO9Z0KpLaP1J9Bl5bfB49YtQVhpSd+7ylfP3zqe4rDik/kSk6VNALyLiZ609JaAPSVlZxXSbkdeE1p9EpwHnQXJb5zhnD+wIrTrNoLaD6JTSCXAqLq0+uDrECYpIU6eAXkTEb0fODnbl7gIgOT6ZcRnjQutw10I4vtM5TkqHgReEOEOJSvGJFTcKW/1CSN0ZY5R2IyL1ooBeRMTPvTo/uctkWsS1CK3DVa7V+WFXQkJSaP1J9HKn3Wx4G/KPh9Sdu7rSJ7s/wVobUn8i0rR5FtAbY7oZY542xuwzxhQaYzKNMX8xxrSpRx9XGGP+aoyZb4zJMcZYY8x/azi/l/+c6r5CryEmIs3Gp7uDqRIhp9sU5sL6N4Jtpds0bZ2HQyd/OdKSAlj3v5C6G5cxjpT4FAB25+5mR/aOUGcoIk1YvBedGGP6AguBjsCbwEZgPPB94DxjzGRr7ZE6dPULYARwAtgD1LW8xBfAG1U8/2UdrxeRZu5owVFWH1oNgMEwtdvU0Dpc90bF2vNdRofWn0S/UdfC+3c7x6v+C2O/1eCuEuMSmdx1Mh/u/BBw0m76tO7jxSxFpAnyaoX+CZxg/k5r7aXW2ruttWcBfwYGAg/UsZ8fAAOAVsCt9Rh/tbX2viq+XqvPNyEizdf8PfMps2UAjOw4krZJbUPrcOWzweNR16r2fHMw7CrwJTjHe1dAVmhrSto1VkTqKuSA3hjTB5gJZAKPV3r5V8BJ4HpjTGptfVlr51lrt1glC4pII/t0j4fpNllfwp5lzrEvAUZ8PbT+JDaktoPBFwbb7jd1DTC161R8xvkz/cWhLzhacDSk/kSk6fJihf4s/+MH1vqXt/ystbnA50AKMNGDsarTxRjzHWPMPf7H4WEcS0SamMLSQhbsXRBou+uAN4g7kBt8EaS2D60/iR1jbgger3kZivIa3FWbpDaM7DASAIvlsz2fhTY3EWmyvAjoB/ofN1fz+hb/4wAPxqrOOcDfcFJ7/gZ8YYyZZ4zpEcYxRaSJWJa1jPySfAB6tOxB7/TeDe+sKA++eDnYdgd40vT1mgZt/D8/Bdmw/s2QulPajYjUhRcBfbr/Mbua18ufb+3BWJXlAb8BxgBt/F9nAPOA6cDcuqT6ABhjVlT1Rd1vzBWRGOXp7rDr34BC/6+9tn2gV4g310ps8flgzDeD7RXPhNSdO6BfuG8hhaWFIfUnIk1TY9ShL//L6HlevLX2oLX2XmvtSmvtcf/XZzg5/UuAfsDNXo8rIk1HmS3zdnfYFa50m9HfdAK8ZmTtnmyeW5QZ+Hrri30Ul5bVfmFTMvJa8PmLyO1eDAc3NLir3um96dmqJwD5Jfks2b/EixmKSBPjRdnK8hX49Gpeb1XpvLCz1pYYY54CJgDTgEfqcM2Yqp73r9Kr3pxIE7Xu8DoO5B0AIL1FOiM7jmx4Zwc3OAEcOAFdM6s9/8mmg3zrmWWUVVq+uWBYZx67ZlRon3zEkrSOMPB82PCW0175HzjvwQZ3d2b3M3lm3TMAzN01l2ndpnkwSRFpSrxYOtrkf6wuR76//7G6HPtwOeR/rFPKjYg0Tx/t+ihwPL3bdBLKyw42xPJ/B48HXeAEds3E3uP53PXy6lOCeYDZa/fz9OeZjT6niHLfO7H6hZBujp3RY0bgeN6ueZSUlYQwMRFpirwI6Of5H2caYyr0Z4xpCUwG8oHFHoxVH+VVdbY38rgiEiOstXy0MxjQn9PznIZ3VpgLX7wYbI+5MYSZxZbCklJue34lx/OKAejYsgXXTezB5H7tAuc8+O4GVuxsRmUX+5wJbXo5xwXH4cvXG9zV8A7D6ZjsvDk8VniMVQdXhT4/EWlSQg7orbXbgA+AXsDtlV6+H2eF/D/W2pMAxpgEY8wg/+6yITHGTDDGJFbx/Fk4m1QB/DfUcUSkadpyfAu7cncBkBKfwsQuIVTXXfMyFOY4x+36Q5/poU8wRvxu9ga+2H0cgHif4YlrR/PbS4fx9A3jGNG9NQAlZZbbn1/F4RPN5KZOnw/G3hRsL/0HNHCLFZ/xcVaPswLt8t1jRUTKeXW31m3AQeBRY8wbxpgHjTEf4wTVm4Gfu87tCmwA5lbuxBhzqTHmGWPMM4B//2wmlT9njHm40iUPAXuNMa8aY/7s/5rr77sF8Etr7UKPvkcRaWLm7gz+GprWbRot4lo0rCNrYelTwfb4W5rNzrALtx7m2UU7A+27vzKIsb2cXXZbxMfx+DWjaJ3ipDFl5RRw31vrIjLPiBh1HcQnOcdZa4KbjTXA2T3PDhzP3TU3sKuxiAh4FND7V+nHAs/g3Ij6I6Av8CgwyVp7pI5djQS+6f861/9cH9dzV1Q6/zmcajbjgFtw3lj0B14Bpllrf9ugb0hEmoUPdwVXOt0BU71lLoBD/komCakw4uoQZxY7/jk/mNV47pBO3DSlYg3/bm1S+PPXRgba767dz97j+Y01vchKaQvDXH+2lv6jwV2N6TSG9BZO7YmDeQf58vCXoc5ORJoQz+qpWWt3W2tvtNZ2ttYmWmt7Wmu/b609Wum8TGutsdb2qqKP+/yvVffVq9L5/7LWXmit7WWtTbPWtrDW9rDWfs1aO9+r701Emp6dOTvZcszZ9y7Rl8jUriHUi1/2z+DxiKshqbqiX03LjsMnmbfJqT9gDPzsK4OrrGRz5sCOgXz6Mgv/XbzzlHOarHG3BI/XvQEnDjaom3hfPGd2PzPQdt/MLSLSvAoki4j4zd0VTLc5vevppCSkNKyjnH2w4Z1ge/wt1Z/bxPxnUWbgePqADvRqX31RsW9O6hU4fnHpLgqKS8M4syjSZSR0G+8clxXDymdrPL0m7pu2P9r5EbaBOfki0vQooBeRZsmz6jbL/w3WH5z2mgodB4c4s9hworCE15bvCbRvmNy7hrNhxuBOdGuTDMDxvGLeWr0vrPOLKuO/HTxe9jSUFjeomwmdJ5Ca4Lxp2p27m83HGrsatIhEKwX0ItLs7Duxj7WH1wIQb+I5o9sZDeuoOB+W/yvYHtd8Nqb+38o95BY69dD7tE9lar/2NZ4f5zN8Y1LPQPvfCzObzwrzaZdAqn9Pgtx9sP7NBnXTIq4F07oGN5VStRsRKaeAXkSaHXcgNKHLhMDNhvW25mXI89/zn94DBl3oweyin7WWZxdmBtrfmNQTn6/2qj5Xje1OUoLzZ2fD/hyWZR4L1xSjS3wijHOVsFz0eINLWM7sNTNwPCdzTvN5UyQiNVJALyLNzpzMOYHjc3ueW8OZNbAWFj0RbE/4DsTFhziz2PD51iNsO3QSgLQW8Xx1TLc6Xdc6JZHLRgXPdb8paPLG3gTlZVH3rYTdSxrUzZSuU0iOd1KXMnMylXYjIoACehFpZvae2BtMt/HFV9iwp162zoXDm5zjxDQYfb1HM4x+s1btDRx/dXRXWiYl1Pnab54eTLv5cMMBcgsalk8ec9I6wPCrgu1FjzWom6T4JKZ3nx5ou9+cikjzpYBeRJqVDzOD6TYTO09seLqNOyAb/Y1mU6qysKSUD9ZnBdqXj67b6ny5QRmtOK1zKwCKSsqYu6FhZRxj0iTXZuob3oGjOxrUjftTpQ93fqi0GxFRQC8izUuFdJteDUy3ObAets9zjo3PSbdpJhZsOUxugXMzbLc2yQzvVv83MhcM7xw4fmfNfs/mFvU6Doa+5Z8IWVjy9wZ1M7nrZFLinTKrSrsREVBALyLNyJ7cPXx5xNlhs/JGPfWy6PHg8aALoU2v0CcXI2a7AvALhneuciOp2lwwLBjQf7b5EDnNJe0GKq7Sr3oO8ut/Y7DSbkSkMgX0ItJsfLDzg8Dx6V1Ob1i6TfYep7pNuUl3eDCz2FBQXMqH6w8E2hcO69Kgfnq1T2VoV3/aTWkZH7n6bPL6zoAO/r0Kik7Asqca1I370yVVuxERBfQi0mx4km6z6Alnx0+AHpOgxwQPZhYb5m85HKg936NtSiAob4gLXG8GZjentBtjYPL3g+3Ff4OivHp3M7nr5MAmU7tyd7Hh6AavZigiMUgBvYg0CztzdrL+yHrASbdxpyzUWd5RWPFMsD3lB57MLVbMXhPc3bWh6TaB691pN1sOkZ3fjNJuhl0B6d2d47zDsPr5enfRIq5FhZSx9zPf92p2IhKDFNCLSLPw3o73AsdTu06lVWIDVpeX/hOKnfrrdBwC/WfWfH4Tckq6jevG1obo0S6FEf4baotLLR+sy6rliiYkLgFO/16w/fmjUFr/NzRf6f2VwPF7O96jzJZ5MTsRiUEK6EWkybPWMnv77ED7/D7n17+TopOw5G/B9pQfOOkTzcQnmw5xsqgUgN7tUwOlJ0PhrnYze20zSrsBGHU9pLRzjrN3wZf/q3cXk7pMonWL1gBkncxi1cFVHk5QRGKJAnoRafI2Ht1IZk4mACnxKZzR7Yz6d7LyOcg/6hy37gFDLvNugjFgjmsF/fxhGSGl2wT7CQb0n2893Lyq3SSmwITvBtsL/gxl9VthT/AlMLNn8FMi96dQItK8KKAXkSbv3R3vBo5n9JhBcnxy/TooLoDPHwm2T78T4uI9ml30Ky4t4+ONwQ2gzhsSWrpNuW5tgjfWFpdaPtl0yJN+Y8a4m51dhgEObYBNs2s+vwruT5vmZM6huKwZvSkSkQAF9CLSpJXZsgoBvTvvuM5WPQe5/htC0zrBqOs8ml1sWLbjaOCm1c7pSSFVt6ls5mkZgeMPm1P5SoCUtjD2W8H2Jw/Ve5V+VMdRdErpBMDxwuMs2rfIyxmKSIxQQC8iTdqKAys4mOesLrdp0YaJXSbWr4OSQicdotzkuyChniv8Me4DV6A987ROnqTbBPob0ilwPG/jQQpLSj3rOyacfickOLu+cmAtbHq35vMr8Rkf5/cOrtK737yKSPOhgF5EmjR3gDOz10wSfAn162DVc5Cz1zlO7Qhjb/RwdtHP2ooVaGYOyajh7Pob2KklPdo6Ae2JwhIWbz/qaf9RL61DxVX6Tx+Cem4S5U67+XjXx+QV17+uvYjENgX0ItJkFZcW8+HODwPtC/pcUL8OSgphvmt1fspdzW51ft2+HPZlFwDQKime8b3betq/MYZzTguu0jer8pXlJn8fyu/ryFoDm+p3c+vANgPpk94HgPySfD7Z/Ym38xORqKeAXkSarM/2fkZ2YTYAnVM7M6LDiPp1sOq/kLPHOU7tCGOa1+o8VEy3OWtQRxLivP+zMdMV0H+04QBlZfVboY55aR1h3E3B9icP1muV3hhTIe3m7e1vezk7EYkBCuhFpMl6e1swsLmwz4X4TD1+5RUXwPw/BtuT73RKDTYz4Uy3KTemZxvapiYCcCCnkDV7s8MyTlQ7/U6IT3KOs9bAxnfqdbn706eF+xZyOP+wl7MTkSingF5EmqTjBcf5dM+ngfZFfS+qXwfLnqqUO/+tms9vgnYfzWNjVi4AifE+pg3oEJZx4uN8zBjUMdBulmk3LTs5ZSzLffxbKKv7DcLdWnZjTKcxgFPZyb2Rmog0fQroRaRJei/zPUrKSgAY3mE4vdN71/3igpyKq/Nn/D9ITPV4htHPnW4zuW870lqEr/Z+hTz65la+styUH7rq0m+ENa/U6/JL+l4SOH5r21tezkxEopwCehFpktzpNhf3ubh+Fy96vOKusKO/6eHMYkdjpNuUm9q/A0kJzp+krQdPsP3QibCOF5VS28GkO4LtT34HJUV1vvycnufQIq4FAJuPbWbT0U1ez1BEopQCehFpcrZnb2ft4bUAJPgSOK/3eXW/+ORhWPRYsD39HohP9HiG0e/oySKWZTpvaoyBGYM71nJFaJIT45jWP5jS0+w2mSo36XZI9lcSOr4LVjxT50vTEtM4q8dZgbZW6UWaDwX0ItLkuFfnp3efTnqL9LpfPP9PUORfHe4wGIZf5fHsYsPcDQcoLzYzukcbOrZMCvuY7k8Bmm3aTVIrmPqjYPuz/4PCun9a4U67mb19diDtTESaNgX0ItKklNky3tkerBByUZ963Ax7dAcs+2ewfdYvwBfn4exih3uF3J3fHk5nDeqIz78J7cpdxziYW9Ao40adcTdDq67O8cmDsPCvdb50QucJdEh2Puk4UnCEhfsWhmOGIhJlFNCLSJOyeP9isk46ud9tWrRhStcpdb/4o/ug1J+z3G08DKrnRlRNRH5RKZ9tORRoz2ykgL5taiLjejnpJtbC3A0HG2XcqJOQBGfeE2wvfBRy9tfp0nhffIUSlm9sfcPjyYlINFJALyJNyqwtswLHF/S5gIS4hLpduGsJrH8j2D73ASd5vBmav+UQBcVlAPTrmEafDmmNNrY77abZ5tEDjPg6dBrqHBfnOWUs68iddjNv9zyOFhz1enYiEmUU0ItIk3G84Dhzd80NtC/rf1ndLrQWPvh5sD3kcug+3uPZxQ53IN1Yq/NVjbdg62FOFDbTHHBfHMx0BfGrn4f9a+p0ab82/RjeYTgAJWUlvLOtfptUiUjsUUAvIk3GO9vfobisGIBh7YcxoM2Aul247n+wZ5lzHJcIZ/8qTDOMfiWlZXy0ofHz58t1b5vCoIyWABSVlPHZ5kO1XNGE9T0T+p/rb/jfdFpbp0sv73d54HjW1lnYOl4nIrFJAb2INAnWWv639X+Bdp1X54vz4cP7gu0J34U2vTydWyxZsfMYx/KcN0UdW7ZgRLfWjT6HCtVumuOusW4zfwPGf2P2js9g07t1uuy83ueRHJ8MwNbjW1lzuG6r+yISmxTQi0iTsO7IOrYc2wJAcnwyX+n1lbpduOAvkL3LOU5uW7FkYDP0QaXqNj5f499H4E67mbvxIEUlZY0+h6jRYSCMvTHYfv9nzpvQWqQmpHJer+D+C+57S0Sk6VFALyJNwutbXg8cn9PzHNIS63Aj59EdsODPwfbZv4Lk1t5PLkaUlVneWxusphLu3WGrM6RLK7q2dlaXcwtK+Hzb4YjMI2qc+XNIbuMcH98Jnz9ap8su7x9Mu3lvx3vkFeeFY3YiEgUU0ItIzMsrzuO9He8F2u5ApkZzfg6lhc5xl1Ew6vowzC52rN5znH3ZTu331ikJnN63XUTmYYzh/GHBNxPvrqlbycYmK6UtnPXLYHvBn+DYzlovG9FhBL3TewOQV5LHnMw54ZqhiESYZwG9MaabMeZpY8w+Y0yhMSbTGPMXY0ybevRxhTHmr8aY+caYHGOMNcb8tw7XnW6MedcYc9QYk2eMWWOMucsY0zx3hBFpZt7PfJ+TxScB6NWqF6M7jq79oi0fwqbZwfb5DzfbTaTKuQPnmad1IiEucms+5w/rHDj+YP0BikubcdoNwJgbIMOpXENJAcy5p8bTwXlj5L459rXNr4VpciISaZ78tjbG9AVWADcCS4E/A9uB7wOLjDF1Xeb5BXAHMBLYW8exLwE+A6YBs4DHgUT/HF6q8zchIjHrlU2vBI6vGHAFprb68cUF8N7/C7ZHXQfdxoZpdrHBWsu7rnQbd0AdCSO7tw6k3WTnF/P51maeduOLc950ltv4jvOmtBYX97uYBJ+zF8Oaw2vYcGRDuGYoIhHk1fLLE0BH4E5r7aXW2ruttWfhBNUDgQfq2M8PgAFAK+DW2k42xrQC/gmUAtOttTdZa3+C84ZgEXCFMebq+n4zIhI71h1ex7oj6wBI9CVW2FSnWvMfhqPbneMW6TDjvvBNMEas2h1Mt0lPTmByv/YRnY8xhq8MdaXdrG3maTcAPSbAiGuC7dk/hKKTNV7SNqkt5/Q8J9B+ZfMrNZwtIrEq5IDeGNMHmAlk4qyOu/0KOAlcb4xJra0va+08a+0WW/eCuVcAHYCXrLXLXf0U4Kz2Qx3eGIhI7Hp508uB43N7nUvrpNY1X3Bwo1PZptzZv4K0DmGZWyyJpnSbcucPV9rNKc75tesG2V3wye9rveRrA78WOJ69fTYnik6Ea3YiEiFe/MY+y//4gbW2wm9ba20u8DmQAkz0YKzqxn6/itc+A/KA040xLcIwtohEWE5RToWbYa8aeFXNF5SVwdvfB//mU3SfAGNurPmaZsBay3tfBuu9uwPpSBrVvTVd0pMAOJ5XzMJtRyI8oyiQ1gHO+U2wvejxWneQHdVxFP1a9wMgvySft7e/Hc4ZikgEeBHQD/Q/bq7m9S3+xzpu2ejN2NbaEmAHEA/0qa0jY8yKqr6AQZ7OWEQ88/a2tykoddJEBrQZwIgOI2q+YOWzsHuxc+yLhwv/Ar7Ir0RH2urdx9l73Klt3iopnsl9I5tuU84Yw1dcufzNvtpNuVHXQc8pzrEt9b9JLa32dGNMhTe7r2x6RTvHijQxXvwlS/c/ZlfzevnzrT0YK5rGFpEIstZWuBn2awO/VvPNsDn74MNfBduTvw+dTgvjDGPHu5VqzyfGR8+bHPfNuXPWZyntBsAYuOgvEJfotPethCV/q/GSi/pcVGHn2JUHV4Z5kiLSmBrjt3b5X9hILAfUeWxr7ZiqvoCN4Z2iiDTEsqxlbM92bmxNiU/hgj4XVH+ytfDWnVDof4/ftg9M+0kjzDL6lZZZ3vpiX6B9QYSr21RWOe3m002HIjyjKNG+P0z9cbA999dweGu1p6clplX4f+TljS9Xe66IxB4vAvryVfD0al5vVek8L0VybBGJoOc3PB84vqjvRaQm1HDf/ernYWt5iT8DlzwOCcnhnWCMWLjtMAdynM212qUmMqV/dKTblPP5DBeP7Bpoz1pVp4rGzcOUH0CnYc5xSQG8eVuNqTfum2M/3PkhB04eCPcMRaSReBHQb/I/Vpcj39//WF2OfVjGNsbEA72BEpya+CLSROzJ3cO83fMC7WsGXVP9ydl74f2fBdsTvgs9Tw/j7GLLrJXBAPmiEV2iorpNZZePDgb0H244QHZ+cQRnE0XiE+HSJ5z7QQB2L4HFT1Z7+qC2gwKbrpXYkgoVokQktnnxm7v8r+pMY0yF/owxLYHJQD6w2IOxKvvY/3heFa9Nw6mus9BaWxiGsUUkQl7c+CLWn0l3epfT6dO6mvverXVuGCzMcdpt+8CMextpltEvr6iE99cFq9u4A+doMqBTS4Z0cT5wLSop4z3VpA/qPLxi6s3Hv4HDW6o9/brTrgscv7b5NQpL9edRpCkIOaC31m4DPgB6AbdXevl+IBX4j7X2JIAxJsEYM8i/u2yoXgMOA1cbYwLbPBpjkoDf+pvVL1eISMzJK85j1pZZgfa1g6+t/uRlT52aapOYEt4JxpA567LIK3JSNPp2SGVY1+qyFyPvslHBNxv/U9pNRVN/VDH15n+3QGnVn2Kc2f1MOqc690kcKzzGu9vfbaxZikgYefXZ6m3AQeBRY8wbxpgHjTEf4+z8uhn4uevcrsAGYG7lTowxlxpjnjHGPAPc7X96UvlzxpiH3edba3OAW4A44BNjzFPGmD8Aq4FJOAG/PlMUaULe2vYWucW5APRs1ZMpXadUfeKhTfDBL4Ltibcp1aaS/7nSbS4f3a3mKkERdvHILsT5nPkt3XGU3UfzIjyjKBKfCJc9Cb4Ep71vFXzyYNWn+uL5+qCvB9rPb3heJSxFmgBPAnr/Kv1Y4BlgAvAjoC/wKDDJWlvX3UBGAt/0f53rf66P67krqhj7DeAMnI2kvgp8DygGfghcXY9dZ0UkypXZsgo3w3590NfxmSp+jZUUwus3OauVAB2HKNWmkoM5BXy+9XCgfemo6Ey3KdexZRJTXTfsvqFV+ooyhlX8GZ//J8j8vMpTL+9/OUlxTuWgTcc2sfzA8irPE5HY4dndT9ba3dbaG621na21idbantba71trj1Y6L9Naa6y1varo4z7/a9V9nXKN/7rPrbXnW2vbWGuTrbXDrLV/ttZWf7u/iMScz/d+TmZOJgBpCWlc2u/Sqk/8+LeQtdY5jmsBX30KEpIaZY6x4s3V+yjzL3dM7NOWrq2jv+qPO+1m1qq9WlmubNId0Huav2Fh1ncg//gpp6W3SOeivhcF2v9d/9/GmZ+IhE30lTMQEanGM+ueCRxf2u/SqktVbv0IFj4abJ/za20gVYm1lldX7A60Lx/VLYKzqbuZp2WQ1sKp6LL98ElW7DwW4RlFGZ8PLv0bJLV22tm74e07nZvDK3HfezJv9zwyszMbZ44iEhYK6EUkJqw7vI6lWUsBiDNxXH/a9aeelLMP/vftYLvvDBj/7VPPa+aW7zzG5gMnAEhJjOMrwzIiPKO6SU6M46IRwY2vXliyK4KziVLpXeGiR4Lt9W86N4dX0rd1X6Z1c1bzLZZn1z/bWDMUkTBQQC8iMeHf6/4dOD6317l0SetS8YTSEnjtJsjz37KTlgGX/d1ZtZQKnl+8M3B8yciutExKiOBs6uea8T0Dx++s3c+xk0URnE2UGnIpjL0p2J5zj3OjbCU3DLkhcPzW1rc4nH/4lHNEJDboL52IRL3dubv5cOeHgfaNQ2889aR5D8Cuhc6x8cEV/4K0Do00w9hx9GQR764N1p6/dkKPCM6m/oZ1S2d4N6e8ZlFJGa+v3BPhGUWpc38HGcOd49IiePUGKKi4afrYTmMZ2m4oAEVlRbyw4YVGnqSIeEUBvYhEvefWP0eZLQNgUudJDGo7qOIJG9+FBX8Kts+8B3pVU86ymXttxW6KSp1/yxHdWzM0imvPV8f9JuT5Jbt0c2xVEpLgymcgsaXTPpYJs26FsrLAKcaYCm+OX970MnnFKgcqEosU0ItIVDtWcKzCRlI3DL2h4gmHNlfKmz8LpvyocSYXY8rKbIW881hbnS930YgutPTfHLvj8EkWbatrZeRmpl1fuOSvwfam2TC/wnYuzOgxg+4tuwOQU5TDrK2zEJHYo4BeRKLa8xuep6DUqSc/qO0gJnWeFHyxIAdevhaKnI2mSO8Blz+lvPlqLNx2hMwjzgpsy6R4LhrepZYrolNKYjyXjw6WsHx+qW6OrdaQy5xyluXm/Q42vR9oxvni+MZp3wi0n1n3DMXV7DIrItFLf/VEJGrlFuVWyOu9cciNwd1My8rgjVvh8GanHZ8MV/8XUttFYKax4bnFmYHjr47uRnJiXOQmE6JrJgRvjp3zZRYHcwoiOJsod/b9FevT/+8WOLw18PIl/S6hbVJbALJOZvHWtrciMEkRCYUCehGJWi9ufJHcYmf1vWernpzb69zgi/MegI3vBNsX/xU6j2jkGcaOzMMn+WD9gUA7VtNtyg3MaMm4Xm0AKCmzPLMwM7ITimZx8XDFM84nWACFOfDi1yDfqeOfHJ/MN4d8M3D6U2ufoqSsJAITFZGGUkAvIlEprziP59Y/F2jfPOxm4nz+FeUvXqqYCzzxdhh+ZSPPMLY8tWB7YH+haQM60L9Ty8hOyAM3TekdOP7v4p2cKFQQWq3UdvC15yDev2Pyka3wyjfAn17ztYFfI72Fc4P0nhN7eG/He5GaqYg0gAJ6EYlKr2x6heOFxwHomtaVC/pc4LywcxG89b3gif3OcXaDlWodOVHIq8uD5R2/M61PBGfjnXNOy6BXuxQAcgpKeGXZ7lquaOa6jITL/hZs7/gMZv8IrCU1IZXrBl8XeOmfa/9JaVlp489RRBpEAb2IRJ2CkgKeWfdMoP2tod8iwZcAR7Y5N8GW+jcT6jAYrnjaSSmQaj23eCeFJU65wiFdWnF636Zxn0Gcz3Dz1OCbk38t2EFJaVkNVwhDLoOzfhFsr3wWFj4KwDWDryEtIQ2AHdk7+HDXh1X1ICJRSAG9iESdVze/ypECpxRhp5ROXNrvUjhxEJ67LLgTbEp7uOZlSGoVuYnGgPyiUv6zKLgz7Len9QneWNwEXDGmG21TEwHYezyf2Wv3R3hGMWDqj2H414LtD++FNa/QKrEVXx/09cDTf//i71qlF4kRCuhFJKrkFefx1NqnAu0bh95IYkkhPH8FHPcHpvHJ8PUXoU3PanqRcq+v3MPRk84nGl1bJ3PBsM4RnpG3khLi+Mak4M/BP+dv10ZTtTHGuYm85+Tgc2/cBtvmcf1p15McnwzA1uNbmZM5J0KTFJH6UEAvIlHlhY0vcLTgKOCszl/R52Ln5r39XzgnGJ+TZtN9fARnGRuKS8v4+2fbAu2bpvQmPq7p/dr/xqRetIh3vq8v9+bw6eZDEZ5RDIhvAVc/76StAZQVw8vX0ebozgq59E988YQq3ojEgKb3m11EYlZOUQ5Pf/l0oP3dYd+mxZu3w7aPgydd+GcYdH4EZhd7Xl2+h91H8wFonZLAVeO6R3hG4dE2NZGvub63P324Wav0dZHcBq57HVr5N+kqOgH/vZwbMqbQMtGpgrQzZ6fq0ovEAAX0IhI1/rPuP+T6d33t3rI7l2z4GNa/GTzhjLthzA2RmVyMKSgu5a8fbwm0v3tGX9JaNN2bh28/s19glX7Nnmw+2nAwwjOKEeldnaA+ySlZSd4RWr14DTf0uSRwyt+++BtF5Teii0hUUkAvIlHhWMGxCnXnb6UNCV+8GDxhwndh+t0RmFlsemnpLvZnO7untk9LrJBn3hR1apXE9ROD3+MfP9hEWZlW6euk42C49nVISHXaufu5btF/aZPoBPn7T+7ntc2vRXCCIlIbBfQiEhX+ufaf5JXkAdA3viXnr3HtAjvqOjj3QedmPqlVflEpj80L5s7fNr0fKYlNd3W+3Hen9yUl0dl8bGNWLu9+qYo3ddZ9nHOjeVwLAFKO7+KmnBOBl/+x5h+cLD4ZqdmJSC0U0ItIxO3O3c2LG4Or8Xfs3U5ceWPI5XDRo+DTr6u6+s+iTA6fKAQgo1US10zoEeEZNY72aS244fRegfafP9xMqVbp667PGc5usj7nzd/XsjLp6C/rf6TgSIW9IUQkuugvpIhE3CMrHwlU0hhZUMiMPOdGTgZfBJf/A3xxNVwtbsdOFvHEJ8HV+TvO6kdSQvP59/v2tD609N8rsO3QSV7W7rH1M+BcuOLf4IsnyVq+d+RI4KVn1z3LwTzdmyASjRTQi0hEfXHoiwq1rn909BgGYPDFTmARlxCxucWiP364iez8YgB6tE3hqrFNs7JNdVqnJPLtacHdYx/+YBPZecURnFEMOu1iuPIZ8MVz0YmTDCx0bojNL8nn8dWPR3ZuIlIlBfQiEjHWWv647OFAe+aJk4wsLPIH808rmK+n9ftyeGHJrkD7FxcMJjG++f2av2VaH7q2djZHOnqyiL/M3RzhGcWgwRfBlc8Q54vnh0ePB56etWUWm4/p31Mk2jS/3/QiEjXm7niPVYdWAxBvLXcdy4ahVyiYbwBrLfe/vY7ylPGp/dtzzmmdIjupCElKiOPnFwwOtP+zaCdbDuRGcEYxavBF8LXnOb3YMtmfBmex/Onz+1TnXyTKKKAXkYgoyM3i4c/uCbSvzsml+4jrnZx5BfP19u7aLJbscHbYjfMZ7r3wNEwzrgr0laEZTOzTFoDSMsuv31mvILQhBp4H173GD3OL8Pn//T4/spZPlz4S4YmJiJsCehFpfNl7+PeL57PXlAKQXlrKdwZe7ewCqxtg6y23oJgHZq8PtL8xqSf9O7WM4IwizxjDry4ags//nmb+lsO892VWZCcVq3pPY8A1/+Ny170ID639O4VL/h7BSYmImwJ6EWlc+9ew7+lz+FdCYeCpOztNpfXM36vOfAM99P5G9vk3kWqbmshdZw+I8Iyiw+DOrbh2QnCzqXvf/JJjJ7XjaYN0G8udFz9HK38Zyz0J8Ty78LfwwS+hrCyycxMRBfQi0ojWvQFPn8vDLYoo9NeVH5ycwVe/8oSC+QZatO0I/10cvBH2vouHkJ6slKVyPzlvIBmtkgA4fKKIX7+zvpYrpDptuo3njlHfC7Sfat2KrCWPw2s3QHF+5CYmIgroRaQRlJXBvN/Bq99kUVwpH6amBF66Z/r/Eac0mwbJKyrhp6+vCbTPHtyJi4Z3juCMok+rpAQeuGxooD1r1V7mbjgQwRnFtiuHf4sBrfsBkO/z8XDb1rD+TXj2Yjh5OLKTE2nGFNCLSHgVnoBXrodPH6LAGH7bvm3gpYv6XMTIjiMjN7cY98cPNrPraB4ALZPieeCyoc36RtjqzBjcictGdQ2075m1NlCrX+on3hfPzyb8PNCek5bKguQk2LMU/nkm7FsducmJNGMK6EUkfI7thH/NhI3vAPCP1q3YleCkg7RMaMkPxvwgkrOLaZ9tPsS/FuwItH954Wl08qeWyKnuvfA02qclAnAgp5B7Zq1V1ZsGGpsxlgv7XBho/7ZdW/KMgeO7nP/fV/4ngrMTaZ4U0ItIeGz/xFmxO7gOgK0JCfy7devAy3eNuYsOKR0iM7cYdzC3gB++sjrQPmNAB64c0y1yE4oBbVIT+e2lwdSb2Wv28+LS3RGcUWz78dgfk94iHYC9CfH8rb3//+XSQnjre/DmHVBcEMEZijQvCuhFxFulJTD31/CfSyHvCABlcYncP2AsJTgroiM7jOSKAVdEcJKxq7TM8oOXV3P4hFOtpUPLFjx85Qil2tTBeUM7c82EHoH2/W+vY2NWTgRnFLvaJbfjR2N+FGj/p2UKGzIGBk9Y9Rw8PROOZTb+5ESaIQX0IuKd47vhmfNh/h/BH7yT2pFXz/4Rq/P2Ak4O7q8m/Qqf0a+fhnjyk618vtV5o2QM/OVrI+nQskWEZxU77r3wNAZlODX6C0vKuOOFVeQVlUR4VrHp0n6XMi5jHACltoz7uvakZNhVwRP2fwF/PwM2z4nQDEWaD/1FFRFvbHgb/jYZdi8JPtdnOnuuf5U/bv9f4KlvDf0W/dr0i8AEY9+8TQf504ebA+3bp/djcr/2EZxR7ElKiOOxa0aRnOBUVtp68AQ/eXWN8ukbwBjDvRPvJdHn3Juw/uhG/t1/HFzwR/D5S6cWHIcXroLZP4aivMhNVqSJU0AvIqEpLnD+WL98HRRkO8+ZOJhxL2XXvs4vVz9CfolTo7p3em++PfzbEZxs7Np6MJc7X1hFmT/uHNerDXed3T+yk4pR/Tq25P5LhgTas9fu59G5WyM4o9jVK70Xt468NdB+4osn2dR3KnzrfWgVrCzEsn/C36fB3pURmKVI0+dZQG+M6WaMedoYs88YU2iMyTTG/MUY0yZc/RhjehljbA1fL3n1/YlIFfYsd/5IL/tn8Ln07nDjezD1R7yw6SWWH1gOQJyJ44HJD9AiTukh9XXsZBE3Pbuc3EInNaRLehJPXDuG+DityTTUVWO7881JwV1k//zRZt5duz+CM4pdNwy5geHthwNQUlbCzxf8nOLOI+A782FQsBoOR7bAv86BT//g3GsjIp4xXnzMaIzpCywEOgJvAhuB8cCZwCZgsrX2iNf9GGN6ATuAL4A3qujyS2vtaw39vvxjrBg9evToFStWhNKNSNNSnO9sFLXoMbCubd8HXQiXPAbJbcjMzuTKt6+koNSpdHHLsFu4c/SdEZpw7CosKeWGp5exaLvzqy85IY7Xbp3EkC7pEZ5Z7CspLeOGfy9jwVZnQ6SkBB8vf3sSI7q3juzEYtCO7B1c+faVFJYWAvCd4d/hjlF3gLWw+nl476dQdCJ4QdexcPk/oF3fCM1YJKrVu8qBV8s7T+AE4Xdaay+11t5trT0L+DMwEHggzP2sttbeV8VXSMG8iFRh1xL42xRY+GgwmE9IhQv+BF/7LyS3obi0mJ/N/1kgmB/QZgC3jri1hk6lKuUVbcqDeYA/XTVCwbxH4uN8PH7NaHq3TwWgoLiMG59ZxtaDJ2q5Uirrnd6bO0cF37A/tfYpVh9c7dy5Peo6+O4C6D4xeMHe5fDkZPj8ESjVJl8ioQo5oDfG9AFmApnA45Ve/hVwErjeGJPaGP2ISJgU5cH798DT58IRV75x7zPgtkUw7ibnjzfw19V/5csjXwJOVZsHpjxAQlxCJGYds6y1/OKNtby7Nivw3I9nDuArwzpHcFZNT3pKAk99cyytU5yfz6Mni/jGv5aw93h+hGcWe6477TrGdBoDQKkt5aef/ZScIn9Z0La94cZ3Yca94It3nivJhw/vhX+cCXv0KbhIKLxYoT/L//iBte7P3sFamwt8DqQAEytf6GE/XYwx3zHG3ON/HF7fb0JEqmEtbHgHHp8Aix8nUI4ysSVc+Bf4xpvQJpiLvHDvQv795b8D7btG38WgtoMad84xzlrLH+ZsqrDx0Q2n9+L2M1UdKBz6dkjj3zeMIyXRqXyzL7uA6/+1hCMnCiM8s9jiMz5+N+V3tEx0yoLuO7mP3yz6TbCCkC8Opv4Ibp4LnYKbfHFgLTw1A979CRRoXwCRhvAioC/fSWJzNa9v8T8OCGM/5wB/w0nJ+RvwhTFmnjGmRxXnVskYs6KqL0CRiDRfh7fC81fAy9dC9q7g831nOKvyY28MrMoDHMk/wj0L7gm0J3eZzPWnXd+YM4551lr+b84mnvxkW+C5y0Z15d4LT9PmUWE0qkcb/n79GBLinH/j7YdO8vV/LuZgrnY7rY8uaV24b9J9gfb7me/zxtY3Kp00Er79CZx9P8Qn+5+0sPQf8Ph4WP+Ws5AgInXmRUBfnsyZXc3r5c+3DkM/ecBvgDFAG//XGcA8YDowVyk68v/bu+/4uKo77+OfM31GvVqyJFvuHdzAgDHVcYAU4pCQBmRJIAshIYRk0zYOkOVJdvehPJRQlk0jTjYhQIDsJlTTjMEsboC7XGVLlmTVkTSjaef548yMui1LI41G+r1fr3nde8/cuXOEsOY7554iBiHQBi/fDg+dBRUvd5a7c+HyX8BVT0F2WbeXhCNhfrT+R9T7TX/vXFcud557pywgdQq01tz5Pzt5qEuYXzmnkH//zGlYLBLmh9uKGQXc9/lFxP5T76lp5fOPvsOxZgn1p2JV+apuK0H//N2fs7dxb/eTrHY49xa46R2YvrKz3FsNT1wNj38Sjn0wMhUWYgwYiU/a2KfQUL9u97qO1rpWa/0TrfVmrXVT9PEGpi/+RmA6cN1ALq61XtLXAzPTjhDjQyQCHzwJD54B6++FSGywmoKlX4VvbjID3PpoKX5428NsqNoQP/7ZuT8j3y2LHg1UJKL5ybPb+eX6A/GylXMKefCLi7HL9JQj5rIFxdz7uYVYo6l+//E2rnz0bSobZFGkU/G9M77H1KypAPhCPm597Va8AW/vE3PK4UtPwhW/hLTCzvIDb8AjK+C5b4K3ZmQqLUQKS8SnRKzlvL9pFzJ7nDfc10FrHQL+M3p43snOF0IA+16Fxy6Ap74KLUc7y0vPNLfHP34PeHL7fOnrla/z6PuPxo+vX3A9y0uWD299xxB/MMxNf9jM7945FC+7dH4RD31pCa7oiqZi5Fy+sIRffHFRvPvN4YZ2Pv3wBj44ctKPHxHltrm5+/y7cUe71BxsOciP1/+47xV5lYIFn4FvvAtnXG8WpgNAw+bH4YHF8ObdZhE7IUSfEhHod0e3/fWRjy1l2F/f+ERfJ6YuupUuN0KcSPU2+N1q+N2nzH6MJx8ufwi+8oLp89qPwy2H+eGbP4wfn118NjctvGn46jvGNLQF+NJ/buTvH3bOZvOJ0yfywBcW4bBJy3yyXDK/mEeuWoIjenekztvB5/7jbV7dVZvkmqWO6TnTueOcO+LH6yrX8asPf9X/C9w58LG74MYNMP0jneWBVnjlp+bO4Za1siiVEH1IxKfFq9HtKqW6d5ZVSmUAywEf8M4IXScmNhvO/gGeL8T40nAAnrrOrPS6b11nuc0Fy2+Jdq/5Elj6/zPRGmjlW69+C2/Q3EovTivm3877N6wWaVUeiIpaL1c8vIFNhxrjZdcuL+f/fW6hrAI7Clw8ZwK/++qZZLrMNIvtgTDXPf4ev91wsO+WZtHLpVMu5ao5V8WP799yP28eefPELyqcDVc9acbqFHSZl6L5MDx7kxk4+/4TEAkPU62FSD1D/sTQWu8DXgTKgZ7NcndgWsgf11q3ASil7Eqp2dFVYQd9nei1limlHD3rpJS6CPh29HDt4H4yIcao43vhLzfCA0vggz93lisLLL4GvrkZPnIHuLNPeJlwJMz33vgeFU1mTnq7xc49F9xDjitnGCs/djz/YTWXP/gWB46bP2lKwZqPz+W2T8yL998Wybdsah5Pf/0cSrJN15FwRHPbc9v5zp+34Q9KoByIW5feyuLCxQBEdIR/euOfeg+S7cv0lXDDW/Cxu8GT11nesA+evh4ePge2P2PG/ggxzqlEtDJEw/kGzCqvzwI7gWXAhZguMudoreuj55YDB4BDWuvywV4nev5rwDzgNeBItPg0Oue0X6O1vnOIP9umxYsXL960SRa9ECmuZge8eRds/0vnCq8xsz9uFnwpmNX3a/vwb+/+G2t3dn5f/tm5P+MT0z6RqNqOWaFwhHte2tNtJhuX3cK9Vy6URaNGsVqvn+t++x7vd+lHP29iJo9ctYSyXE8Sa5YajvuO88X/+SLVbdUAlKSX8PvLfk+eO+8kr4zq8MLGR2DDA+DvMZZhwgJYcSvMvdzMdS9E6jvlVp2EBHoApVQZ8FPgEiAPqAaeAe7QWjd0Oa+cfgL9qVwneu5XgdXAfCAfsAM1wNvAg1rrk9zXG9DPJYFepLaqrSbI7/xr7+fKV8BFa2DSslO65BO7n+Bf3vmX+PF1C67jW4u/NcSKjn2VDe3c8qet3brYTMr18OjVS5hTnHmCV4rRwB8Ms+aZD/nzpiPxsgynjTtXz+fyhSVJrFlq2N2wm2v+fg3tITNj0KLCRTy26jGcVufAL+Jrgrd/Ae88ZPrWd5UzBc75Jiz8Ethdiau4ECMveYF+rJJAL1JSJAJ7XzAffAf7+F47fSWc971TDvIArx5+lVteu4VItJV/5aSV3H3B3TLf/En8dVsVP/rLB3j9nQP6zptZwP2fX0i2p1fPQTFKaa1Zu/EwP/3rdoLhzs/PKxaXcsfl80h32pJYu9HvtcrXuHndzejoDNQrJ63krvPvOvVxN231sOE+2PgfEPJ1fy6tAJbdAGdcd9Kug0KMUhLoE00CvUgpgTbY+gd452HTz7SnWZfBed+FkiWDuvyW2i1c/+L1dIQ7AJiTO4ffXPIbPHbpctCfOm8Htz33IX/7oHMWG6tF8e2VM7jxgunSXz5Fba1s4ub/2sLhLvPTl2S7+fmnF3DezIIk1mz0++3233LXe3fFj6+ceSU/PuvHg1sJubUO3n0U3n0M/E3dn3Okm9b6M6+H/Bl9vlyIUUoCfaJJoBcpoeEAbPqNefT8UFNW07d0xa1QtGDQb1HRWME1z18TXxymLKOMxy99XBaP6ofWmue2VXH7c9tpbA/Gy8ty3dz3+UUsniSDh1Od1x/ktue28/Tmo93Kr1xayj9fNpcsjz1JNRvdtNb83/f+L7/b8bt42dcXfp0bT79x8Bft8Jo569/+Rfd1NGKmXQRnfg1mrJJ+9iIVSKBPNAn0YtQKB2HP8/Der7pPOxnjzIIlXzYfYtllQ3qrQy2HuPb5a6nzmeUdcl25rL10LWWZQ7vuWFVR6+W257bzVkV9t/Irl5ay5uNzyXBJ0BtLnttWxW3Pftjti1temoMfXDqbKxaXYpG7ML1EdIQfvvlD/nbgb/Gy753xPa6ee/XQLhwKwIdPwlv3QV0fC71nTzJdcRZeBWkDHJArxMiTQJ9oEujFqNNUaVqiNj8Orcd6P59TDmd9HRZ+EZwZQ367Sm8l1z5/LTXtZvl1j83Dry/5NXPz5g752mON1x/kwXUV/HL9AUKRzr+t0hVj7Dve2sFtz27nfz6o7la+ZHIOd3xyHvNL+lsEffwKhoN8Y9032FC1IV72o2U/4guzvzD0i2sN+18zXXH2/L33zF4WO8y+DBZdA9MulFZ7MdpIoE80CfRiVOhohV3/bfrHH3gD6PnvVsH0i2HpV2DmJQn7cKpqreLa56+lqq0KAJfVxUMrH+KMojMScv2xIhiO8IeNh7nvlb00tAXi5RYFXz6nnO+smiWDJceJ5z88xh1/3U51s79b+epFJXxn1UxKc2S8SVftwXZufPlGNtdujpfddvZtfGbmZxL3Jo2HzJ3Mzb8FX2Pv5zNLTAPIwi9B7pTEva8QgyeBPtEk0IukiYTNDDXb/gg7noNgW+9z0gph8dWw+MuQMzmhb1/preT6F6/naKvpj+q0Onnw4gc5q/isk7xy/AiFIzy3rYoH1lXEF4iKOaM8h59ePl+moxyH2gMhHlhXwX++ub/bTDgOm4Wrz5rMP543lcJMmVYxpi3Yxtde+hrv170fL1tz1hqunHVlYt8o6IMPnzJjjY78b9/nTDoHFnwG5q0GT25i31+IgZNAn2gS6MWI0hqObobtT5sFoPoa3IWCqRfA0mvNrDXWxPfH3te0j+tfvD7eZ95usfPARQ+wvGR5wt8rFQVCEf6y5QgPvbaPQ/Xt3Z4ryXbzTx+dxeULJw5u1g4xZuyra+Vf/76Ll3bUdCt32Cx8bmkZN1wwLb4C7XjXEmjhay9+je312+Nlty65lWvnXzs8b1i7E7asNQ0m7cd7P2+xmel9F3wWZl0KjrThqYcQfZNAn2gS6MWw0xqqtpgAv/0ZaD7c93n5s2DhF2DBlZA1fIvY7KjfwQ0v3UBjh7k17bQ6ufeCe1lRumLY3jNV+INh/vxeJY+8vp+jTd3nvs5w2fjGhdP58jnluOzSH1d02ri/np/9fRfbKpu6ldutiisWl/L1C6YzKU+64jR3NHPjyzfywfEP4mX/eNo/ctPCm4bvy3EoYCYX2LIWKl7q3dcewO4xXRnnfhKmfwSc6cNTFyE6SaBPNAn0YliEQ1C5EXb/zfSNbzzY93mePNNCdPrnoXghDHOL74aqDdz62q20Rbv3eGweHrz4wXHfZ77O28Ef3z3M2o2HqGnp6PZcltvOV5ZP4R+Wl5PlltlrRN+01qzbVcv96yp6BXurRXHZgmKuOXsySyfnjOs7O23BNr7xyjd4r+a9eNlnZ36WHy37ETbLMI9Daa01DSsf/Ln/Ljk2F0y7GOZ8AmZdAm6ZflYMCwn0iSaBXiRMoM1ML7nrb6ZFyNfQ93muLJj9CZi/GqacPyxdavryTMUz3LHhDkLarGSa6cjkkZWPsKBg8HPXpzKtNe8dauTxtw/x/IfV3fpCg5mW8LoVU7n67Mky4FUMmNaa9RXHeeCVCt492PtvwOyiDK45u5zLF04kbZz+f+UL+bj1tVtZf3R9vGxFyQruOv+ukVvErmE/fPAUfPAEHN/T9zkWG0xeDjM/aua3z5s+7I0uYtyQQJ9oEujFoGlt5kGueAX2vQIH34JwR9/nOrNg9sfMQKypF4DNMWLVjOgIj2x7hIe3PRwvm+CZwMMrH2ZGzvhbXdHrD/Lctip+9/Yhdh3z9nq+MMPJ186byheXTcLjGJ+BSyTGO/vreXBdBesrevfhznDauGJJKV9aNokZE4Y+/WyqCYaD/GTDT/jv/f8dL5uTO4cHL36QQk/hyFVEa6jZbu6k7ngOarf3f25OuQn2M1ZB+blgl/ERYtAk0CeaBHpxSnyNZu7jildMa3yfg1qjMorNYKtZH4MpK8DmHLFqxrQH2/nn9f/My4dfjpfNypnFLy7+BRPSJox4fZIlGI7w+u46/rL1KC/vqKEj1Lsf7dLJOVx99mQumV+E0yZ95EXibK9qZu07h3hmSxW+YLjX8/NLMvnUwhI+efrEcTU7jtaaB7Y8wGMfPBYvK3AXcO+F93J6wenJqVT9Ptj5V9j5HBw9QS6wuWHKeTDjI2ZwbU65tN6LUyGBPtEk0IsTCnWYP+r7Xzet8Ec39T2oKqZwrpmZZvZlULwILJaRq2sPld5Kbl53MxVNFfGycyaew93n3026Y+wP+tJas6WyiWe2HOWv26q6rfIZ47Zb+dSiEq46axLzJsrCQGJ4NfuCPLXpCGvfOcT+472nqbUoWD49n9WLSvjovKJx0yXnyT1Pcuc7dxLW5suO3WJnzVlrWD1jdXIr1lIFe1+CvS+ahpxAa//nZpWZgF++wjTgZJWOWDVFSpJAn2gS6EU3gXYzWOrQW6YLzZH/7b8bDZiuNFPPN4s+TbsYsstGrq4nsO7wOta8tYaWQEu87Ko5V/Gdpd8Z/oFnSRQKR3j3QAMv7qjhxe3HqOqx+E/M3OJMPrOklCuWlMpAVzHiIhHNhn31/OHdQ7y8s5ZAH3eMnDYLK2bks2puERfPKSQvfeTv8I2kd6rf4buvf5fmjuZ42RUzruAHZ/4Al20U3LUIBeDw2ybc732x/373MblTo+E+GvIzxs8dUTEgEugTTQL9ONfhNbPRHHzLhPijmyHSuyW3k4KSJZ0BvmQJWEdPQA6Gg9yz6R7W7lwbL3NYHKw5ew2fmv6p5FVsGLV1hFhfcZwXth9j3a5amvpoiQcoznJx+cISVi8qYVbR+OuzLEanZl+Q5z+s5i9bjvLO/r4H0lsULC3PZdXcCayaWzRmp8Cs9FbyrVe/xd7GvfGyGTkzuOv8u5iaNTWJNetDwwGoeNmE+0MbTtx6D5A/E8qWdT7yZ0gXnfFNAn2iSaAfRyJhqNsNR98zLe9H3jOLj3CSfyO506B8uRnMOvXCUbu64IHmA/zwzR92W7ilOK2Yu8+/e0zNZBOJaHZUt/DG3jre2FPHpkONvWaoicl02bhkfhGrF5WybEouFot8gIrR62iTj+e2VvHs1qN9DtiOmZKfxooZ+ayYUcDZ0/LG1CxM7cF2bn/7dv5+4O/xMrfNzQ/O/AGrp68enVN+hoNmrZEDb5jVvw+/A6G+7w7GuXOg9EwoO9ME/JLFsrjV+CKBPtEk0I9hrbWmz3ssvB/dDIH+PyTjCmabqcomn2O2mcXDX9chiOgI/7Xrv7h30710dOkedEHZBdy5/E6ynKndN1xrzeGGdjYeaOCtiuOs33uc+rZAv+cXZ7lMS+a8Is6ckovdmrxxDEIM1sHjbby0o4YXdxzjvUON9PdRbrMoFk/O4bwZ+SybmsdppVkpP6hba81Te5/i5xt/TiDS+W/9/NLzuf2c28l35yexdgMQ6jCfObGAf+R/Idz/3ywAlBWK5sPExTBxEUxcaMZkjdC0xmLESaBPNAn0Y4DW0FwJ1e9D9TY4Ft16q0/+WmWBwnkmvJcvNwE+bZR/WHRR6a3kjrfvYGP1xniZzWLj24u/zdVzrx6drVknobWmoraVjQcaeDf6ONZy4tau2UUZrJwzgY/OK2J+SWZK/txC9KfO28G6XTW8uL2GDfvq+5wpJ8Zps7BoUjbLpuSxbEouiybl4HakZsDf3bCb777+XQ62HIyXZTuz+eGZP+TSKZemzr/zQLtpwa/cCJXvmm1/65R0ZXXChHmdAX/iItPgJCF/LJBAn2gS6FNMKAD1FVC7ozO4V28z00kORPoEKD0DSpeabfHClFzmOxQJ8fiOx3l468P4w51hd2bOTH527s+YlTsribU7Nc3tQbYeaWLr4Sa2VDaytbKp337wMXlpjniXgxUz8sfVVH9ifOsIhdl0sJE39h7njT117KhuOeH5NotidnEGp5dmc3pZNgvLsplWkI41Rbqf+UI+7tt8H7/f+ftu5eeWnMuas9YwMX1ikmo2BFqb6TErN3aG/LqdA3ut1QmFc2DCfBP2J8wz+2l5w1tnkWgS6BNNAv0oFYlA82Go2WHCe+0O09/9+N6TDFrtwuaG4tNMcC9ZYrZZpSk/EGlzzWZ+/u7P2dWwK15mURb+Yd4/cNPCm3BYR27RqlPV3B5ke3UzO6pa2FHVwrYjTeyr6z19X08ZThtLy3M4c0oeK2bkM7c4U/rDC4FpvV9fUcc7+xrYeKCeg/XtJ31NutPGgpKsaMDP4rTSbIqzXKO6xfvtqrdZ89Yaatpr4mVum5sbTr+Bq+ZcNar/7g2Ir9G04ldtNdvqrdB0eOCvzyjuHvALZpuVbR1jcwD1GCCBPtEk0CdZqMMswX18L9TvNdvje8zg1ZPNGtCVM8uE9+LTOx9508GSmrea+3Ks7Rj3bLqn22AxMAtF3X7O7czPn5+kmvWmtaaq2c+Oqha2VzVHty0cbfIN6PXZHjtnludy5pRczpqax5zizJRpURQimWpa/NHuavVs3N/A3tqB/R3N9tiZXZTB7KJM5hSb7cwJGaOqu05roJX7Nt/Hn3b/Cd1lMoNJGZP4/pnf57zS85JYu2HQVm+CfdWWaMjfZrqXDpgyUynnzzKz7BTM7NyXFv1kk0CfaBLoR4DWZoDq8T3R0F4R3e4xLRAnWqipL1mTorcc53WG9zG8Sp834OXXH/6atTvX4gt1BmKn1cmNp9/INfOuwW5JTp/KWHDfW+OlorY1/thb20qzb2B3UmwWxZziTBaWZbNoUjaLJuVQnucZ1a2FQqSKZl+QD440s+1IE1srzaPOe4K1NbpQCqbkpTE7GvBnFKYztSCdyXkeXPbkBf2ttVu54+07ui2aB3B28dncsuQW5ubNTVLNRkBbPdRuh5rtUPOh2dbuPPmsOj158kywz58JBbNMA1juVMielJRVzcchCfSJJoE+QcJBaD4CjQeg8WD3R8MB6DhxP88+uXNNaC+c2xngC2aDKzOxdR+l/CE/T+x+gsc+eIymjqZuz62avIrvLP3OiPUfbe0Icai+jUP17Rw43sa+2lYq6kx4bw/0P0CvJ7tVMXNCBvMmZjK3OJP5JVnML8lKajgQYjzRWlPd7GdbZRNbjzSxrbKJD4+20NoRGvA1LApKczxMK0hjWoEJ+dMK0phakE5+umNEvowHI0H+tOtPPLT1IbzB7rOXXVp+KV9f+HXKs8qHvR6jQiRs7nTHAn7NdnOXu/HAqTeYoUzX1NwpkDPFhPz4/hRwyhoeCSKBPtEk0A9QJAJttdB81PRtb+gR3JuPgB54sOsUuyU4E/JmQP50sy2YDemFY7bV/UR8IR9/3v1nfr391xz3He/23KycWXz/zO9zRtEZCX1PrTWN7UGONvo4WN/Gofo2Dta3x7cDbdHrKsNlY25xJnMnZjJvYhZzizOZXpiOwybTSAoxmmitOdLoY9cxL7uqW9h1zMvOYy0cPN5G5BQjRLrTRlmuh7IcN5NyPUzK81CW46Es10NpjjvhX94b/A08sOUBnt77NJEu4VWhWDl5JdctuG5st9ifSKxLa93uaHfW3Z37oYF1f+wlraAz3GeVmc/vrFJz5zyrVPrsD5wE+kSTQB/lbzahvPmo6aPXcrTHcdXAB6P2xZlpbunlz4gG9+gjdyrY3Yn7OVJYk7+JJ/Y8we93/p4Gf/cpzUrSS/jGom9w2ZTLsKhTD8ThiKamxc/RJh9HG31m22W/qsl3Si3tXWV77MwoTGd6YTrTCzOYXpjOjML0UT/ITghxYr5AmL21XnZVe9l1zMu+ulb2H2/lSKOv33nxT2ZCppNJuZ5o6Dchf2K2m6IsF8VZLjyOwS2Stb9pP/dvuZ9XDr/S67nlE5dz3YLrWDJhifxNAtNA13IE6vaYrq/Hd5vg33DAfO6fbLHFE/HkR0N+mem+kxUN/NllkDHRdPWxSKMOEugTb8wH+kgY2o6bOdlba8B7zGy7BfYjA1tw6WQyJpq+7F0fuVMge/K4bW0fiH1N+/jjrj/y7L5nu/WRByh0F/KVBV/hszM/2+8sDv5gmNqWDmq8fmpa/NS0dFDbYvarmv0cbfRxrMVP+FSb2rqwWxVlOR4m53mYnJfGtII0phdmMGNCOnlpI3OLXQgxOviDYQ7Wt7Gvto39da3RoG+64rUNsmEgJsttpzjLFQ34boqjQb84qzP0p51gZdxtddt4dNujvHn0zV7PLSxYyDXzruGCsguSNu5o1At1mLFtsYDfeKBzv+nQyRfIOhmL3czIk1kc3U6EjCKTH7qWjf2GPgn0iZaygT4cNANNW4+ZkB4L6vH9Y+CtMd1kTrkPXT/cOdFba2W9g3v2pPHwDzBh/CE/Lx16iSf3PMnm2s29ni/yFPH5mV9mWcEltPigvjVAfWsHda0d1LR0UNPip7alg2Mt/gEPPj2ZdKeNkmw3k/I8lEeDe3leGpPzPEzMdsssM0KIE9Ja09AWoLLRx+GGdiqjj8PRR3Xz0BoWYjwOK/npTgoynBSkO8nPcFCQ7qIgw0l+uoOCDCfN4UM8d3Atr1S+1K0rDkC+O5/V01fz6RmfpjSjdMj1GTciYXO3vmG/CfdNleYOflOl6YrbUgWRgY/FOCFXdpfgP9E0CqYXmi4/6YWQFj1256RqY6EE+kQbNYE+Ejbz0LbVmRb1tjpor48ex8pi5ccHvpDSQNnckFViAntmaTS4dz0uAUdaYt9zHAlHNF5/kPdr9vDMvqdYf+wFfOHed0VsoRJoPp/munlEdGL7muanOyjJdlOS4zbbbHOruyTHTWm2h0y3TVrahRDDJhiOUN3kN2G/0YT8qiYf1c1+qpt9HGv2EwwnNrNkpDfhyn8Dv2sjqO53DxSK2VlLuGTyai6efCGF6Z5RNU1nyomETW+AeNA/3Bn4W45CSzV0NCf2PS02E/K7Bf2CzsAfey4t33T3GT2r7EqgT7SkBPq63fDaz7uHdF9D4lrSe3Lnmlta6RM6t5kTo6E9Gtg9uan6LXdEhcIRWvwhmtoDNPmCNLcHafIFaGoP0tgepDla3tQejD4foCFQjd+xBVvm+1hdVb2uqbWFkHcuwcZlhNunc6r/zm0WRWGGk8JMFxMynUzIdHV5OE1oz078YDQhhEikSERT3xbgWDTgm6Dv51izj6pmP8ea/Rxr8RMInfpnpbI1Y8/eiD37PSz23rOu6ZCHoHceqm0h2ZbZ5Hrc5KY5yPbYyU1zkOMx+5kuO1luO5luO5lum9l32fE4rNIgMhCBNhPsvdFHS1WX/S7liWrp78mZZebg9+SbkD/9YjjjuuF5rxOTQJ9oSQn0VVvhP84f4kWU+daZUdQ7rGcUQXqsvFDmlI2KRDStgRCt/hBefwivP2i2HZ37rV3KW/whWjui50RDfIt/YH9klL0BW8YH2DPfx+o+2nd9ArkEm84g2LQUHe49FViW205euoP8NCd56Q6zn+6kKBrWC6PhPdfjkFVThRDjgtYab0eIOm8Hdd4Ojrd29N6PbutbA4R6dfEJY0vfhT3nXaxpe1Cqd0aKhNIIeecTallAuH0qcPJBnDaLMiHfZesS+E3Y7xr8s9x2Mlw2Mlw20pw20qOPNKcNu1UGiwJm0G57PXiroiG/ClrrTBfi1lrTCBrbDmZK7K6WfgU+fm9i6n1qTvlDe3DDxcXwSivou9yVbb4xxm8P5Xe/XZTW5didM6ZWQe1LJKLxh8K0dYRpD4Q6t4Ew7R0h2gPdj9uix15/iNaOztAeC/CtgdCgZ2Y4uRBWzyFs6buxpu3G6qrp+zRtJS10GiW2C5mStZD8Ujf50bCeFw3u+elOcjwOmd5RCCF6UEqZkOyyM60g/YTnRiKaJl+wW9hvbA/Q2DaLhvZLqW6r4kDHqzSotwhbmuKvs9jacORsxJGzER3yEGqbQahtJuHWmX02vgCEImb8QEPb4AeNOm2WbkG/Z+DPcNlIc9hId9lId1pJd9pJc1rjr/HYbbgdVjwOK267NXUbeiwW020mvcAsHHkiQX806HcN/F2Po92U24733RPCkz98P0eCSQv9SSSlhT4UgB3PdA/tnjyw9T2LyWgVC9y+QBh/KGK2wdgjgi+67wuG6YhufYEI7cEQ7R1h2gJm2x7sHshjwX2w0ygOJ6UwrSweG2meRpRnHz7rdpr0DkL0vVKfTdk4Z+JyLpnyUS4su5B0x4k/hIQQQoyciI7wft37PH/weV48+CJ1vrp+z81Q5aRH5mPtmEWwrZQWH7T4g/iDw9Rldghcdgsehw233YR8j8OKK77fJfw7rHjsts79eHnna93RLwkuuxWX3YLLloJfGCIR8DeZcN9+3NwFyJ0GE5KyToF0uUm0UTModghC4QiBcISOYNetCdXdy8N9HncN3/EwHgh3C+v+6LE/2Fk2mH6MyZbmsJLhspMeveWZ4Yre/nR2Hqd32c90mdYQj0NRHzzIrqZtbKvbyqaaTb3miu/KbrGzrHgZl5RfwoWTLiTTMT5WtxVCiFQW0RG21G7hhYMv8PKhl08Y7u0WO/Py5rF4wmJOy1/I1PQFhMMuWvxBWnxBmn1BWvwhWnxdj4O0+Mxd5LYOs43tJ2ACoBHlsFpw2i04bdGQ3yXsu+xWnDZT5ow9Fz2v1/l2K05b9LwuzzlsFpw2i9lazbHDZhkrM65JoE+0ZAT6Om8HT28+Qkc0FHeEwtFtJL7t6LO8ZyA320RMAzZaxVsWnFbSHKYFIc0Z3UZbGLoex87rFtZdNjKcJsQP5A9BREeo9Fayo35H/LG9fjttwbYTvq4kvYRzS85lRckKzig6A49dVswTQohUpbVmd+Nu1h9dz/qj69lau5XwCVZEVyimZU9jbt5c5ubNZV7ePGblzsJtO/mUzlprfMGwCfh+c6fa2xGkrSNMa0eQ1o6w+QLg7/4lILbf6jd3tX1Bc4d7NN4xSBSbRcXDfSzwO6wWHLbOLwHOeFmXc2wWHFbzxSH23GmlWayY0U836OElgT7RkhHod1a3cOl9vRe9SEXu6Dfszltx0WNH9Nt4dOt2dH5r7zOcO82tvTSnjTSHFU/0eLi/iXsDXvY17aOiqYJ9TfvY3bibnfU7aQ22nvS1GY4MFhcu5qziszi35FwmZ06WWQ6EEGKM8ga8bKzeyPqj69lUs4mDLQdP+hqLsjA1aypz8+YyLXsa07OnMy17GsVpxYNa9XugIhHzBcEXvaseG3MW3w+G8QViY9E6z/EFe5aZ41j3WX8wgj8YpiMF79D35ZqzJ/PTy+cn461lUOxYkOjBjhZF/HZV7BaYw2pua3W7ZWWzdn5z7VHudnQJ49Fg7u5yq6xrWectMktKBNhgOMjR1qNUeis57D1MpbeSA80HqGiqoLa9dsDXmeCZwOIJi1lSuIRFExYxPXv6sP5BFkIIMXpkODJYOXklKyevBKDeV8/W2q1sqt3E5prN7GrY1asFP6IjVDRVUNFU0a3cbXMzLWsaU7OnUpZRRmlGqdmml5Lryh3yZ6vFokwD2QlW1R0KrbXpSRCMxLvjxsJ+LPD7g9Euu9FxdPGy2Hkhs99ZHu52vUC0d0Ig3NlzIdFdfR0pNLNQwlrolVKlwE+BS4A8oBp4BrhDaz3gVY4Gcx2l1DnAj4GzABdQAfwKeEDrE9z/Glh9RryFvrEtwMOv74uG7q7h2tpn2I4FdJe9++2i2NaWQv9DDgdvwMuxtmPm0X4svl/TVsOR1iNUt1X3WinwZHKcOd1um87Nm0tRWlFKfIERQggx8tqD7exs2Nmtq+bB5oNoTi2HeWweSjNKKU03Ib8ko4QJnglM8EygwFNAnisP6xif5a4/WmuCYd1tHGCgR3fl+JeAPp7v/gUhzLIpuVw0e0IyfpTkdLlRSk0DNgCFwLPALuBM4EJgN7Bca10/HNdRSl0OPAX4gT8BDcAngFnAk1rrzw7xZ0v5QbFjkT/kp8HfEH/U++rN1m+2Db4GatprqGmvOWnf9hOxW+yUZ5UzPcvcBp2eM525uRLehRBCDF1bsI1dDbvY07inW/fOpo6mQV/Toizku/Ip8BRQ6Cmk0FNIgbuAXHcuOc4cclw55DhzyHZlk+XIGrfhf5RLWqB/AVgF3Ky1fqBL+T3At4FHtdY3JPo6SqlMTGt8FibsvxctdwHrgLOBL2it/ziEn00CfYKFI2F8IV/80R5qxxvw0hJooaWjBW/Aizfo7dyPPRdoie/7Qr6E1qkorYhJGZMoyyijLKOMyZmTmZY9jbKMMmwW6ZkmhBBiZGitafA3sK9pHwdbDnLEe4RKbyVHWs12KI1UPSkUmc7MeNDPcGSQbk+Pb9Md6WTYM8y2R1maI400W5p8IRgeIx/olVJTgX3AQWCa1p19F5RSGZguMwoo1Fr3+3/hYK6jlPoK8Evgca31l3tc7yLgFeANrfWgl10di4Fea01YhwnrMMFwkEAk0GsbCJtHMBIkGAnGjwORQPy457ntofZuQb3PR9BHIDL4hTUGw2V1UZRWZG5Jpk2gKK3IPDxFTEyfSEl6CS6ba0TrJIQQQpwqrTVNHU3dQv7R1qPUttdS115HbXstjR0D7uWcEA6LA5fNhcvmwm1z47K6Oo+tblNm617msrlwWp04rA7sFjt2i73bvt3auXVYHP3u2yy2sXq3PCmDYi+Kbl/sGsIBtNZepdRbmFb3szABO5HXib3m+T6u9wbQDpyjlHJqrTsG+gMlW1VrFfduupewDhOKhOLhOxzp3IZ0iHAkTERH4vux8yM60nlOj9fFrpXqbBYbua5c8lx55Lpyzb67cz/XlUuBp4AiTxFZzqyx+g9eCCHEOKKUMl1mXDksKFjQ5zmBcIDjvuPUttd2Pny1NPmbaOxopNHfSFNHE43+RloCLUOuUyASIBAIJORag2Gz2LApG1aLFauKPixWLMrSZ3ls32LpfL7rubF9i7Jwbsm5rJ6xOik/16lKRKCfFd3u6ef5vZggPpMTB/rBXKff12itQ0qpA8A8YCqw8wTvjVKqvyb42Sd63XBoC7bx/MG+vqOMDQqF2+bufNjdZNgzyHRkkunMJMORQYbDHHfd73qcbk+XkC6EEEL04LA6mJg+kYnpE096bigSoqmjKR72vQEvrcFWsw20du4HW2kNtOINRsuj+4nu/joYoUiIECEYhrbKAk9S5qAflEQE+qzotrmf52Pl2cNwnUS996gyEv3RLMqCRVnM7avoravY7S6H1dHtuOvzXc/peW7XgO6xebqH9i4Pp9UpYVwIIYRIMpvFRr47n3x3/qBer7WmI9yBP+THH/bHu9f6Q378IT++cOd+7Pmux8FIkGA42K17b2y/v/Ku+6FIKMH/RbpLpamnR2K0Xyy5DXX07WCuM+DXaK2X9HkB03K/+BTec8gK3YX8+3n/3vsWkcXa7+0jm8XW+/bSCV4ngVoIIYQQQ6GUiveNT4aIjpgW+lh3465dj7vsh3SISCRa1nW/6/NduivH9idlTkrKzzUYiQj0sVbwrH6ez+xxXiKvk6j3HlXSHelcOuXSZFdDCCGEEGLUsihLvPfAeJeIewm7o9uZ/Tw/I7rtr2/8UK7T72uUUjZgChAC9p/kvYUQQgghhEhJiQj0r0a3q5Tq3tkoOt3kcsAHvDMM11kX3V7Sx/XOAzzAhlSa4UYIIYQQQohTMeRAr7XeB7wIlAM39Xj6DiANM098bO54u1JqdnRV2EFfJ+pJ4DjweaXU0lhhdGGpO6OHDw/6hxNCCCGEEGKUS9RKsdOADUAh8CxmishlwIWYLjLnaK3ro+eWAweAQ1rr8sFep8trPoUJ9n7gj0AD8EnMlJZPAlfqIfyQY3FhKSGEEEIIMWqd8swlCZmPJ9q6vhT4DSaAfweYBtwPnN0zhCfyOlrrZ4DzMQtJXQF8EwgCtwKfH0qYF0IIIYQQYrRLSAv9WCYt9EIIIYQQYgQlp4VeCCGEEEIIkRwS6IUQQgghhEhhEuiFEEIIIYRIYRLohRBCCCGESGES6IUQQgghhEhhEuiFEEIIIYRIYRLohRBCCCGESGES6IUQQgghhEhhEuiFEEIIIYRIYRLohRBCCCGESGFKa53sOoxqSql6t9udO2fOnGRXRQghhBBCjHGbN2/+g9b6S6fyGgn0J6GUOgBkAgeTXJXxYHZ0uyuptRDDTX7P44P8nsc++R2PD/J7Hnm7JNCLlKWU2gSgtV6S7LqI4SO/5/FBfs9jn/yOxwf5PacG6UMvhBBCCCFECpNAL4QQQgghRAqTQC+EEEIIIUQKk0AvhBBCCCFECpNAL4QQQgghRAqTWW6EEEIIIYRIYdJCL4QQQgghRAqTQC+EEEIIIUQKk0AvhBBCCCFECpNAL4QQQgghRAqTQC+EEEIIIUQKk0AvhBBCCCFECpNAL4QQQgghRAqTQC9SilLql0opHX1MT3Z9xNAopWYopb6vlFqnlKpUSgWUUjVKqWeVUhcmu37i1CmlSpVSv1JKVSmlOpRSB5VS/08plZPsuomhU0rlKaWuU0r9RSlVoZTyKaWalVLrlVJfVUpJrhijlFJXd/n8vS7Z9RHdycJSImUopT4BPAe0AunADK11RXJrJYZCKfVH4HPADmA90ADMAj4JWIFvaa3vT14NxalQSk0DNgCFwLPALuBM4EJgN7Bca12fvBqKoVJK3QA8DFQDrwKHgQnAp4Es4Cngs1rCxZiilCoDPsD8XU4Hrtda/2dyayW6kkAvUoJSqgDzx+Q1oAg4Hwn0KU8p9Q/ANq31lh7l5wMvARoo11pXJ6F64hQppV4AVgE3a60f6FJ+D/Bt4FGt9Q3Jqp8YOqXURUAa8D9a60iX8iLgXaAM+IzW+qkkVVEkmFJKYf4eTwGeBr6LBPpRR26NiVTxH9HtTUmthUgorfVveob5aPnrmC9vDuCcka6XOHVKqamYMH8Q+EWPp28D2oCrlVJpI1w1kUBa63Va6792DfPR8mPAI9HDC0a8YmI43QxcBFyL+XcsRiEJ9GLUi7bifgq4QW7XjyvB6DaU1FqIgbooun2xj7DnBd4CPMBZI10xMWLk3+wYo5SaA/wrcJ/W+o1k10f0TwK9GNWUUpOB+4C1WutnklwdMUKiv/eLgXZAPkRSw6zodk8/z++NbmeOQF3ECFNK2YBroofPJ7MuIjGiv9PfYcZJ/CjJ1REnYUt2BYToT3S2hN9iBsHenOTqiBGilHICvwecwPe01o1JrpIYmKzotrmf52Pl2cNfFZEE/wrMB/6mtX4h2ZURCfETYBFwrtbal+zKiBOTFnoxrKJT1ulTeKzt8vJvYwa/Xi+hbvQa4u+457WsmBah5cCfgLtG6ucQw05FtzITwxijlLoZ+A5mVqOrk1wdkQBKqTMxrfJ3a63fTnZ9xMlJC70YbvsA/ymcXwVmfnLg/wC/1lr/bTgqJhJmUL/jnqJhfi3wWeAJ4CqZ+i6lxFrgs/p5PrPHeWIMUErdhOkWuQO4WGvdkOQqiSHq0tVmD7AmydURAySBXgwrrfXFg3zpPEyXi2uVUtf2c85eM5sWq6V/ffIM4XccF/0A+QMmzP8BuEZrHR7qdcWI2h3d9tdHfkZ0218fe5FilFK3APcCH2LCfG1yayQSJJ3Of8f+6OdsT48ppR7DDJa9ZaQqJvongV6MVgeBX/bz3Mcwc9H/GWiJnitSlFLKgWmRvxx4HLi25ywpIiW8Gt2uUkpZesxRnoHpRuUD3klG5URiKaW+j+k3vxX4iNb6eHJrJBKog/4/fxdj+tWvx3yJl+44o4QsLCVSjlLqNWRhqTEhOgD2aeAyzAfI1yTMpy5ZWGp8UEqtAX4KbAJWSTeb8UMpdTtmXQlZWGqUkRZ6IUQyPYIJ88eBo8BP+ri9+5rW+rURrpcYnK8DG4D7lVIXAzuBZcCFmK42/5zEuokEUEp9GRPmw8CbwM19/Js9qLX+zQhXTYhxTQK9ECKZpkS3+Zgp0vrz2vBXRQyV1nqfUmopJvBdgvmyVg3cD9whLbljQuzfrBW4pZ9zXgd+MxKVEUIY0uVGCCGEEEKIFCbz0AshhBBCCJHCJNALIYQQQgiRwiTQCyGEEEIIkcIk0AshhBBCCJHCJNALIYQQQgiRwiTQCyGEEEIIkcIk0AshhBBCCJHCJNALIYQQQgiRwiTQCyGEEEIIkcIk0AshhBBCCJHCJNALIYQQQgiRwiTQCyGEEEIIkcIk0AshhBBCCJHCJNALIYQQQgiRwiTQCyGEEEIIkcIk0AshhBBCCJHCJNALIYQQQgiRwv4/b/K3HRU5hlcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 266,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu, lmbda= 0, 1\n",
    "\n",
    "xrange = np.linspace(-5, 5, 200)\n",
    "\n",
    "nus = [0.1, 1, 10]\n",
    "for nu in nus:\n",
    "    pdf = students(xrange, mu, lmbda, nu)\n",
    "    plt.plot(xrange, pdf, label=rf\"$\\nu={nu}$\");\n",
    "plt.title(r\"$\\mathrm{St}\"rf\"(x\\vert\\mu={mu}, \\lambda={lmbda}, \\nu)$\", fontsize=15)\n",
    "plt.legend(fontsize=11);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## Estimating the parameters of a stock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Response [200]>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# https://www.alphavantage.co/documentation/\n",
    "url = \"https://www.alphavantage.co/query\"\n",
    "symbol = \"TSLA\"\n",
    "params = {\n",
    "    \"function\": \"TIME_SERIES_DAILY_ADJUSTED\",\n",
    "    \"symbol\": symbol,\n",
    "    \"outputsize\": \"full\",\n",
    "    \"apikey\": apikey\n",
    "}\n",
    "\n",
    "r = requests.get(url, params=params)\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "stock = pd.DataFrame.from_dict(r.json()[\"Time Series (Daily)\"], orient=\"index\", dtype=float)\n",
    "stock.index = pd.to_datetime(stock.index)\n",
    "stock = stock.sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "stock_ret = stock.rename({\"5. adjusted close\": symbol}, axis=1)[symbol].pct_change().dropna()\n",
    "N = len(stock_ret)\n",
    "mu, sigma = stock_ret.mean(), stock_ret.std(ddof=1)\n",
    "N_stock = norm(loc=mu, scale=sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 391
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xrange = np.linspace(stock_ret.min(), stock_ret.max(), 100)\n",
    "sns.histplot(stock_ret, kde=False, stat=\"density\");\n",
    "plt.plot(xrange, N_stock.pdf(xrange), label=\"Adjusted Normal\", c=\"tab:orange\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Student's-t EM\n",
    "\n",
    "In order to estimate the parameters of the Student's-t distribution, we make use of the EM algorithm which involves maximizing the expected complete-data log likelihood given by \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "Q(\\boldsymbol\\theta, \\boldsymbol\\theta^{\\text{old}}) &= -\\frac{N}{2}\\log 2\\pi + \\frac{1}{2}\\sum_{n=1}^N\\mathbb{E}[\\log\\eta_n] - \\frac{N}{2}\\log\\lambda - \\frac{\\lambda}{2}\\sum_{n=1}^N\\mathbb{E}[\\eta_n](x_n - \\mu)^2 \\\\\n",
    "&+ \\frac{N\\nu}{2}\\log\\frac{\\nu}{2} - N\\log\\Gamma\\left(\\frac{\\eta}{2}\\right) + \\left(\\frac{\\nu}{2} - 1\\right)\\sum_{n=1}^N\\mathbb{E}[\\log\\eta_n] - \\frac{\\nu}{2}\\mathbb{E}[\\eta_n]\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "----\n",
    "\n",
    "In the **E** step of the algorithm, we compute the sufficient statistics\n",
    "\n",
    "$$\n",
    "    \\mathbb{E}[\\eta_n] = \\frac{\\nu + 1}{\\nu + \\lambda (x_n - \\mu)^2}\n",
    "$$\n",
    "\n",
    "$$\n",
    "    \\mathbb{E}[\\log\\eta_n] = \\psi\\left(\\frac{1}{2}(\\eta + 1)\\right) - \\log\\left(\\frac{1}{2}[\\eta + \\lambda(x_n - \\mu^2)]\\right)\n",
    "$$\n",
    "\n",
    "\n",
    "--- \n",
    "\n",
    "For the **M** step we update $\\mu$ amd $\\lambda$ as\n",
    "\n",
    "$$\n",
    "\\mu^\\text{new} = \\frac{\\sum_{n=1}^N\\mathbb{E}[\\eta_n]x_n}{\\sum_{n=1}^N\\mathbb{E}[\\eta_n]}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\lambda^\\text{new} = \\left[\\frac{1}{N}\\sum_{n=1}^N\\mathbb{E}[\\eta_n](x_n - \\mu)^2\\right]^{-1}\n",
    "$$\n",
    "\n",
    "In order to find $\\nu^\\text{new}$, we must satisfy the equality\n",
    "\n",
    "$$\n",
    "    \\psi(\\nu/2) - \\log(\\nu/2) = 1 + \\frac{1}{N }\\sum_{n=1}^N\\mathbb{E}[\\log \\eta_n] - \\frac{1}{N}\\sum_{n=1}^N\\mathbb{E}[\\eta_n]\n",
    "$$\n",
    "\n",
    "Which can be easily be acomplished with a numerical method such as the bisection method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "That is, to take an $M$-step in estimating the parameters of student's-t distribution, we require to satisfy the equality\n",
    "\n",
    "$$\n",
    "    \\log a - \\psi(a) = \\frac{1}{N}\\big(N \\log\\mathbb{E}[\\tau] - \\mathbb{E}[\\log\\tau]\\big)\n",
    "$$\n",
    "\n",
    "More generally, we would like to find $a \\in\\mathbb{R}$ that satisfies\n",
    "\n",
    "$$\n",
    "   \\big(\\log a - \\psi(a)\\big) - b = 0\n",
    "$$\n",
    "\n",
    "for any given $b\\in\\mathbb{R}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "class St:\n",
    "    def __init__(self):\n",
    "        pass\n",
    "        \n",
    "    def E_nu(self, X):\n",
    "        return (self.nu + 1) / (self.nu + self.lmbda * (X - self.mu) ** 2)\n",
    "    \n",
    "    def E_log_nu(self, X):\n",
    "        return digamma((self.nu + 1) / 2) - np.log((self.nu + self.lmbda * (X - self.mu) ** 2) / 2)\n",
    "    \n",
    "    def E_step(self, X):\n",
    "        return self.E_nu(X), self.E_log_nu(X)\n",
    "    \n",
    "    @staticmethod\n",
    "    def bisection(f, x_low, x_up, tol=1e-5, max_its=1000):\n",
    "        diff = np.inf\n",
    "        nits = 0\n",
    "        while diff > tol:\n",
    "            if nits >= max_its:\n",
    "                raise ValueError(\"Root searching did not converge\")\n",
    "\n",
    "            x_mid = (x_low + x_up) / 2\n",
    "            f_mid = f(x_mid)\n",
    "\n",
    "            if np.sign(f_mid) == 1:\n",
    "                x_up = x_mid\n",
    "            else:\n",
    "                x_low = x_mid\n",
    "\n",
    "            diff = np.abs(f_mid)\n",
    "            nits += 1\n",
    "\n",
    "        return x_mid\n",
    "\n",
    "    @staticmethod\n",
    "    def nu_root(k, **kwargs):\n",
    "        f = lambda nu: (digamma(nu / 2) - np.log(nu / 2)) - k\n",
    "        return St.bisection(f, **kwargs)\n",
    "    \n",
    "    def expected_log_likelihood(self, X):\n",
    "        N = len(X)\n",
    "        E, E_log = self.E_step(X)\n",
    "        Q = (- N * np.log(2 * np.pi) / 2 + E_log.sum() / 2 + N * self.lmbda / 2\n",
    "             - self.lmbda * (E * (X - self.mu) ** 2).sum() / 2\n",
    "             + N * self.nu * np.log(self.nu / 2) - N * np.log(gamma(self.nu / 2))\n",
    "             + (self.nu / 2 - 1) * E_log.sum() - self.nu * E.sum() / 2)\n",
    "        \n",
    "        return Q\n",
    "    \n",
    "    def M_step(self, X):\n",
    "        E, E_log = self.E_step(X)\n",
    "        mu = (E * X).sum() / E.sum()\n",
    "        lmbda = 1 / (E * (X - self.mu) ** 2).mean()\n",
    "        \n",
    "        cst = 1 + E_log.mean() - E.mean()\n",
    "        nu = self.nu_root(cst, x_low=0, x_up=5)\n",
    "        \n",
    "        self.mu = mu\n",
    "        self.lmbda = lmbda\n",
    "        self.nu = nu\n",
    "    \n",
    "    def fit(self, X, tol=1e-5, maxiter=500):\n",
    "        self.mu, self.lmbda, self.nu = 1, 1, 1\n",
    "        # Change of the expected log likelihood\n",
    "        ell, delta_ell = -np.inf, np.inf\n",
    "        nits = 0\n",
    "        while np.abs(delta_ell) > tol:\n",
    "            if nits >= maxiter:\n",
    "                raise ValueError(\"EM did not converge\")\n",
    "                \n",
    "            new_ell = self.expected_log_likelihood(X)\n",
    "            delta_ell = np.abs(new_ell / ell - 1)\n",
    "            ell = new_ell\n",
    "            self.M_step(X)\n",
    "            \n",
    "            nits += 1\n",
    "            \n",
    "            \n",
    "        return self.nu, self.mu, np.sqrt(1 / self.lmbda)\n",
    "    \n",
    "    def pdf(self, x):\n",
    "        \"\"\"\n",
    "        Generates a function that returns the value\n",
    "        of the pdf of a Student's-t distribution\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        x: float, np.array\n",
    "            Values to evaluate the pdf at\n",
    "        mu: float\n",
    "            The mean of the distribution\n",
    "        lmbda: float\n",
    "            The precision of the distribution\n",
    "        nu: float\n",
    "            The degrees of freedom of the distributino\n",
    "        \"\"\"\n",
    "        const = gamma(self.nu / 2 + 1 / 2) / gamma(self.nu / 2) * np.sqrt(self.lmbda / (np.pi * self.nu))\n",
    "        pdf_x = const * (1 + (self.lmbda * (x - self.mu) ** 2) / self.nu) ** (-self.nu / 2 - 1 / 2)\n",
    "        return pdf_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.88421630859375, 0.0014401408322635076, 0.021464833802201565)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "st = St()\n",
    "st.fit(stock_ret)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 391
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xrange = np.linspace(stock_ret.min(), stock_ret.max(), 300)\n",
    "sns.histplot(stock_ret, kde=False, stat=\"density\", color=\"tab:gray\");\n",
    "plt.plot(xrange, N_stock.pdf(xrange), label=\"Adjusted Normal\", c=\"tab:blue\", linewidth=2)\n",
    "plt.plot(xrange, st.pdf(xrange), label=\"Adjusted St\", c=\"tab:orange\", linewidth=2)\n",
    "plt.legend(fontsize=12);"
   ]
  }
 ],
 "metadata": {
  "hide_code_all_hidden": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
